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NODE6 (E)\Data\2014\Kota\JEE-Advanced\SMP\Phy\Unit-07\Electrostatics\English\Exercise.p
EXERCISE–01 CHECK YOUR GRASP
SELECT THE CORRECT ALTERNATIVE (ONLY ONE CORRECT ANSWER)
Using mass (M), length (L), time (T) and current (A) as fundamental quantities, the dimension of permittivity is : (A) ML –2^ T 2 A (B) M –1^ L –3^ T 4 A 2 (C) MLT –2^ A (D) ML 2 T –1^ A 2
Two point charges + 9e and +e are kept 16 cm. apart from each other. Where should a third charge q be placed between them so that the system is in equilibrium state : (A) 24 cm from + 9e (B) 12 cm from +9e (C) 24 cm from + e (D) 12 cm from + e
Four charges are arranged at the corners of a square ABCD as shown in the figure. The force on the charge kept at the centre O will be :
A (^) B
D–2q +qC
+q +2q
(A) perpendicular to side AB (B) along the diagonal BD (C) along the diagonal AC (D) zero
When charge is given to a soap bubble, it shows : (A) an increase in size (B) sometimes an increase and sometimes a decrease in size (C) no change in size (D) none of these
Two equal negative charges –q are fixed at point (0, –a) and (0, a) on y–axis. A positive charge Q is released from rest at the point (2a, 0) on the x–axis. The charge Q will : (A) execute simple harmonic motion about the origin (B) move to the origin and remain at rest (C) move to infinity (D) execute oscillatory but not simple harmonic motion
Figures below show regular hexagon, the charges are placed at the vertices. In which of the following cases the electric field at the centre is zero.
5q 4q 6q 3q q 2q I
q –q
–q q q q II
2q 2q
q q
2q 2q III
2q 2q q q
2q q IV (A) IV (B) III (C) I (D) II
Two infinite linear charges are placed parallel to each other at a distance 0.1 m from each other. If the linear charge density on each is 5 C/m, then the force acting on a unit length of each linear charge will be : (A) 2.5 N/m (B) 3.25 N/m (C) 4.5 N/m (D) 7.5 N/m
An electron of mass m (^) e , initially at rest, moves through a certain distance in a uniform electric field in time t 1. A proton of mass m (^) p , also, initially at rest, takes time t 2 to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio t 2 /t 1 is nearly equal to : (A) 1 (B) (m (^) p/m (^) e ) 1/ 2^ (C) (m (^) e /m (^) p ) 1/ 2^ (D) 1836
An electron is projected as in figure with kinetic energy K, at an angle = 45° between two charged plates. The magnitude of the electric field so that the electron just fails to strike the upper plate, should be greater than:
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E d 45°
K
(A)
K
qd (B)^
2K
qd (C)^
K
2qd (D) Infinite
1 0. A point charge 50 C is located in the XY plane at the point of position vector r^ 0 ^ 2 iˆ^ 3 jˆmeter. What
is the electric field at the point of position vector r^ ^ 8 iˆ^ 5 jˆ
meter: (A) 1200 V/m (B) 0.04 V/m (C) 900 V/m (D) 4500 V/m
1 1. Three point charges 1C, 2C and 3C are placed at the corners of an equilateral triangle of side 1m. The work required to move these charges to the corners of a smaller equilateral triangle of side 0.5m in two different ways as in fig. (A) and fig. (B) are W (^) a and W (^) b then:
A'
(A)
A 1C
2C B (^) B' C' C 3C
A (^) 1C
B' C'
C 2C (^) (B) 3C B
(A) Wa > W (^) b (B) W (^) a < W (^) b (C) Wa = W (^) b (D) W (^) a = 0 and W (^) b = 0
1 2. As per this diagram a point charge +q is placed at the origin O. Work done in taking another point charge –Q from the point A (0, a) to another point B (a,0) along the straight path AB is : y
O B
A
x
(A) (^ )
qQ (^4) a
a (B) zero (C) (^ )
q Q (^4) a
(D) (^ )
q Q (^4) a
a
1 3. Two identical thin rings, each of radius R meter are coaxially placed at distance R meter apart. If Q 1 and Q (^2) coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of the other is :
(A) zero (B)
1 2 0
q Q Q 2 1 4 2 R
(C)^
0
q 2 Q Q 4 R
(D)
1 2 0
q Q Q 2 1 4 2 R
1 4. Two identical particles of mass m carry a charge Q each. Initially one is at rest on a smooth horizontal plane and the other is projected along the plane directly towards first particle from a large distance with speed v. The closest distance of approach be :
(A)
2 0
1 Q
4 mv (B)
2 2 0
1 4Q
4 mv (C)
2 2 0
1 2Q
4 mv (D)
2 2 0
1 3Q
4 mv
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2 4. The work done in rotating an electric dipole of dipole moment p in an electric field E through an angle from the direction of electric field, is : (A) pE (1 – cos) (B) pE (C) zero (D) – pE cos
2 5. Which one of the following pattern of electric line of force can't possible :
(A) (B) (C) (D)
2 6. A sphere of radius R and charge Q is placed inside an imaginary sphere of radius 2R whose centre coincides with the given sphere. The flux related to imaginary sphere is :
(A) 0
Q
(B)^0
Q
2 (C)^0
4Q
(D)^0
2Q
2 7. Due to a charge inside a cube the electric field is E (^) x = 600 x 1/2^ , E (^) y = 0, E (^) z = 0. The charge inside the cube is (approximately) :
Y 0.1m
O
Z 0.1 m
X
(A) 600 C (B) 60 C (C) 7 C (D) 6 C
2 8. Electric flux through a surface of area 100 m 2 lying in the xy plane is (in V–m) if (^) E ˆi 2 jˆ 3kˆ : (A) 100 (B) 141.4 (C) 173.2 (D) 200
2 9. Two spherical, nonconducting, and very thin shells of uniformly distributed positive charge Q and radius d are located at a distance 10d from each other. A positive point charge q is placed inside one of the shells at a distance d/2 from the center, on the line connecting the centers of the two shells, as shown in the figure. What is the net force on the charge q?
d/2{
Q d
Q
10d
(A) 2
0
qQ 361 d to the left^ (B)^02
qQ 361 d to the right
(C) 2
0
362qQ 361 d to the left^ (D)^02
360qQ 361 d to the right 3 0. A solid metallic sphere has a charge + 3Q. Concentric with this sphere is a conducting spherical shell having charge –Q. The radius of the sphere is a and that of the spherical shell is b (b > a). What is the electric field at a distance R (a < R < b) from the centre?
(A) 2
0
4Q
2 R (B)^02
3Q
4 R (C)^02
3Q
2 R (D)^0
Q
2 R
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3 1. A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10V. The potential at the distance 3 cm from the centre of the sphere is : (A) zero (B) 10 V (C) same as at a point 5 cm away from the surface (D) same as at a point 25 cm away from the surface
3 2. A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of –3Q, the new potential difference between the same two surfaces is : (A) V (B) 2V (C) 4V (D) –2V
3 3. A cube of metal is given a charge (+ Q), which of the following statements is true : (A) Potential at the surface of cube is zero (B) Potential within the cube is zero (C) Electric field is normal to the surface of the cube (D) Electric field varies within the cube
3 4. A metallic solid sphere is placed in a uniform electric field. The lines of force follow the path(s) shown in figure as :
(A) 1 (B) 2 (C) 3 (D) 4
CHE CK Y OU R GR ASP (^) ANSWER KEY E XE R CISE - Q u e. 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 A n s. (^) B B (^) B A D B C B C D C B B B B C A D D Q u e. 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0 3 1 3 2 3 3 3 4 A n s. B C (^) A A A C A C C A B B A C D
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- A circular ring carries a uniformly distributed positive charge. The electric field (E) and potential (V) varies with distance (r) from the centre of the ring along its axis as :
(A)
E
r
(B)
E
r
(C)
V
r
(D)
V
r
- Find the force experienced by the semicircular rod charged with a charge q, placed as shown in figure. Radius of the wire is R and the infinite line of charge with linear charge density (^) is passing through its centre and perpendicular to the plane of rod.
++++
R++
(A) 2
0
q 2 R
(B)^20
q R
(C)^20
q 4 R
(D)^0
q 4 R
- Which of the following is true for the figure showing electric lines of force? (E is electrical field, V is potential)
(A) E A > E B (B) E B > E A (C) V A > V B (D) V B > V A
An electric charge 10 –8^ C is placed at the point (4m, 7m, 2m). At the point (1m, 3m, 2m), the electric : (A) potential will be 18 V (B) field has no Y–component (C) field will be along Z–axis (D) potential will be 1.8 V
Two point charges Q and –Q/4 are separated by a distance x. Then : Q (^) x Q/
(A) potential is zero at a point on the axis which is at a distance x/3 on the right side of the charge –Q/ (B) potential is zero at a point on the axis which is at a distance x/5 on the left side of the charge –Q/ (C) electric field is zero at a point on the axis which is at a distance x on the right side of the charge–Q/ (D) there exist two points on the axis where electric field is zero
1 0. Two positively charged particles X and Y are initially far away from each other and at rest. X begins to move towards Y with some initial velocity. The total momentum and energy of the system are p and E : (A) If Y is fixed, both p and E are conserved (B) If Y is fixed, E is conserved, but not p (C) If both are free to move, p is conserved but not E (D) If both are free, E is conserved, but not p
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1 1. Two particles X and Y, of equal mass and with unequal positive charges, are free to move and are initially far away from each other. With Y at rest, X begins to move towards it with initial velocity u. After a long time, finally : (A) X will stop, Y will move with velocity u (B) X and Y will both move with velocities u/2 each (C) X will stop, Y will move with velocity < u (D) both will move with velocities < u/
1 2. In a uniform electric field, the potential is 10V at the origin of coordinates, and 8V at each of the points (1, 0, 0), (0, 1, 0) and (0, 0, 1). The potential at the point (1, 1, 1) will be : (A) 0 (B) 4V (C) 8V (D) 10V
1 3. Four charges of 1 C , 2 C , 3 C , and – 6 C are placed one at each corner of the square of side 1m. The square lies in the x–y plane with its centre at the origin. (A) The electric potential is zero at the origin. (B) The electric potential is zero everywhere along the x–axis only if the sides of the sqaure are parallel to x and y axis. (C) The electric potential is zero everywhere along the z–axis for any orientation of the square in the x–y plane. (D) The electric potential is not zero along the z–axis except at the origin.
1 4. Potential at a point A is 3 volt and at a point B is 7 volt, an electron is moving towards A from B : (A) It must have some K.E. at B to reach A (B) It need not have any K.E. at B to reach A (C) To reach A it must have more than or equal to 4 eV KE at B (D) When it will reach A, it will have K.E. more than or at least equal to 4 eV if it was released from rest at B
1 5. A particle of charge 1C & mass 1 gm moving with a velocity of 4 m/s is subjected to a uniform electric field of magnitude 300 V/m for 10 sec. Then it's final speed cannot be : (A) 0.5 m/s (B) 4 m/s (C) 3 m/s (D) 6 m/s
1 6. A particle of mass m and charge q is thrown in a region where uniform gravitational field and electric field are present. The path of particle : (A) may be a straight line (B) may be a circle (C) may be a parabola (D) may be a hyperbola
1 7. A horizontal electric feild (E = (mg)/q) exists as shown in figure and a mass m attached at the end of a light rod. If mass m is released from the position shown in figure find the angular velocity of the rod when it passes through the bottom most position :
=45^0 (^) E= m
mg q
m +q
(A)
g (B)^
2g (C)^
3g (D)^
5g 1 8. The diagram shows a small bead of mass m carrying charge q. The bead can freely
+Q a 4a
B A
g
move on the smooth fixed ring placed on a smooth horizontal plane. In the same plane a charge + Q has also been fixed as shown. The potential at the point A due to +Q is V. The velocity with which the bead should proejcted from the point A so that it can complete a circle should be greater than :
(A)
6qV m (B)^
qV m (C)^
3qV m (D) None of these
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2 6. Two short electric dipoles are placed as shown. The energy of electric interaction between these dipoles will be
r
p 1
p 2
(A) 1 32
2Kp p cos r
(B) 1 32
2Kp p cos r
(C) 1 32
2Kp p sin r
(D) 1 32
4Kp p cos r
2 7. Charges Q 1 and Q 2 lies inside and outside respectively of a closed surface S. Let E be the field at any point on S and be the flux of E over S. (A) If Q 1 changes, both E and ^ will change. (B) If Q 2 changes, E will change but ^ will not change. (C) If Q 1 =0 and Q 2 0 then E 0 but =0 (D) If Q 1 0 and Q 2 =0 then E=0 but 0
2 8. An electric dipole is placed at the centre of a sphere. Mark the correct answer : (A) The flux of the electric field passing through the sphere is zero (B) The electric field is zero at every point of the sphere (C) The electric potential is zero everywhere on the sphere (D) The electric potential is zero on a circle on the surface
2 9. An infinite, uniformly charged sheet with surface charge denisty cuts through a spherical Gaussian surface of radius R at a distance x from its center, as shown in the figure. The electric flux through the Gaussian surface is :
x
R
(A)
2 0
R
(B)^
2 2 0
2 R x (C)^
2
0
R x (D)^
2 2 0
R x 3 0. At distance of 5 cm and 10 cm outwards from the surface of a uniformly charged solid sphere, the potentials are 100 V and 75 V respectively. Then : (A) potential at its surface is 150 V (B) the charge on the sphere is (5/3) x 10 –10^ C (C) the electric field on the surface is 1500 V/m (D) the electric potential at its centre is 225 V
3 1. An electric field converges at the origin whose magnitude is given by the expression E = 100r N/C, where r is the distance measured from the origin. (A) Total charge contained in any spherical volume with its centre at origin is negative. (B) Total charge contained at any spherical volume, irrespective of the location of its centre, is negative. (C) Total charge contained in a spherical volume of radius 3 cm with its centre at origin equals 3 × 10 –13^ C. (D) Total charge contained in a spherical volume of radius 3 cm with its centre at origin has magnitude 3 × 10 –9^ C.
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3 2. A bullet of mass m and charge q is fired towards a solid uniformly charged sphere of radius R and total charge
- q. If it strikes the surface of sphere with speed u, find the minimum value of u so that it can penetrate through the sphere. (Neglect all resistnace forces or friction acting on bullet except electrostatic forces)
R
q
+q m
u
(A)
0
q 2 mR (B)^0
q 4 mR (C)^0
q 8 mR (D)^0
3q 4 mR
3 3. A unit positive point charge of mass m is projected with a velocity v inside the tunnel as shown. The tunnel has been made inside a uniformly charged non conducting sphere. The minimum velocity with which the point charge should be projected such that it can it reach the opposite end of the tunnel, is equal to :
R/
(A)
2 1 / 2 0
R
4m
(B)
2 1 / 2 0
R
24m
(C)
2 1 / 2 0
R
6m
(D) zero because the initial and the final points are at same potential
3 4. Three concentric conducting spherical shells have radius r, 2r and 3r and Q 1 , Q 2 and Q 3 are final charges respectively. Innermost and outermost shells are already earthed as shown in figure. choose the wrong statement.
2r
Q 1
3r
r
Q 2
Q 3
(A) Q 1 + Q 3 = –Q 2 (B) Q 1 = 2
Q
(C)
3 1
Q
Q
(D) 3
2
Q 1
Q 3
3 5. Shown in the figure a spherical shell with an inner radius 'a' and an outer radius 'b' is made of conducting material. A point charge +Q is placed at the centre of the spheri- cal shell and a total charge –q is placed on the shell. Charge –q is distributed on the sur- faces as : (A) –Q on the inner surface, –q, on outer surface (B) –Q on the inner surface, –q+Q on the outer surface
b Q a
(C) +Q on the inner surface, –q–Q on the outer surface^ ^ q (D) The charge –q is spread uniformly between the inner and outer surface
3 6. In the previous question assume that the electrostatic potential is zero at an infinite distance from the spherical
shell. The electrostatic potential at a distance R (a < R < b) from the centre of the shell is where 0
K 1
(A) 0 (B)
KQ
a
(B) K
Q q R
(D) K
Q q b
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EXERCISE–03 MISCELLANEOUS TYPE QUESTIONS
TRUE / FALSE
The work done in carrying a point charge from one point to another in an electrostatic field depends on the path along which the point charge is carried.
An electric line of forces in the x–y plane is given by the equation x 2 + y 2 = 1. A particle with unit positive charge, initially at rest at the point x = 1, y = 0 in the x–y plane, will move along the circular line of force.
A small metal ball is suspended in a uniform electric field with the help of an insulated thread. If high energy X– ray beam falls on the ball, the ball will be deflected in the direction of the field.
A ring of radius R carries a uniformly distributed charge +Q. A point charge –q is placed in the axis of the ring at a distance 2R from the centre of the ring released from rest. The particle executes a simple harmonic motion along the axis of the ring.
Two identical metallic spheres of exactly equal masses are taken. One is given a positive charge Q coulomb and the other an equal negative charge. Their masses after charging are different.
FILL IN THE BLANKS
Electric lines .............. (can/can not) have sudden breaks.
Figure shows line of constant potential in a region in which an electric field
(50V)(40V) (30V) (20V)(10V)
A
C
B
is present. The values of the potential are written in brackets. Of the point
A, B and C, the magnitude of the electric field is greatest at the point. ...............
Two small balls having equal positive charge Q (coulamb) on each are suspended by two insulating strings of equal length L (metre) from a hook fixed to a stand. The whole set–up is taken in a satellite into space where there is no gravity (state of weightlessness). The angle between the string is ....... and the tension in each string is ........... newtons.
A point charge q moves from point P to point S along the path PQRS (fig.) Y
X R E
S Q
in a uniform electric field E pointing parallel to the positive direction of the P
X–axis. The coordiante s of points P, Q, R and S (a, b, 0), (2a, 0, 0) (a, –b,
- (0, 0, 0) respectively. The work done by electric field is ..............
The electric potential V at any point x, y, z (all in meters) in space is given by V = 4x 2 volt. The electric field at the point (1m, 0.2 m) is .............. V/m.
Five point charges, each of value +q coulomb, are placed on five vertices of a regular
-q
q q
q
q q
hexagon of side L metre. The magnitude of the force on the point charge of value –q
coulomb placed at the centre of the hexagon is ............ newton.
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M ATCH THE COLUMN
- Two parallel metallic plates have surface charge densities 1 and 2 as shown in figure.
I II III
C o l u m n – I Column–II
(A) If 1 + 2 =0 (p) Electric field in region III is towards right (B) If 1 + 2 > 0 (q) Electric field in region I is zero (C) If 1 + 2 < 0 (r) Electric field in region I is towards right
(s) Nothing can be said
- Column–I shows graphs of electric potential V versus x and y in a certain region for four situations. Column–II shows the range of angle which the electric field vector makes with poisitive x–direction Column–I : V versus x, V versus y Column–II : Range of angle
(A)
450 300 (p) (^0 0) 450
(B)
1350 (q) (^45 0) 900
(C)
450 600 (r)^90 0 1350
(D)
300 600 (s) (^1350) 1800
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- Column–I gives certain situations involving two thin conducting shells connected by a conducting wire via a key K. In all situations one sphere has net charge +q and other sphere has no net charge. After the key K is pressed, column–II gives some resulting effect. Column I Column II
(A)
+q
shell I
initially no net charge
shell II
K (p) Charge flows through connecting wire
(B)
+q
shell I
initially no net charge
shell II
K (q)^ Potential energy of system of spheres decreases
(C)
+q
initially no net charge
shell I shell II
K (^) (r) No heat is produced
(D)
+q initially no net charge
shell I
K
shell II
(s) The sphere I has no charge after equilibrium is reached
- A spherical metallic conductor has a spherical cavity. A positive charge is placed inside the cavity at its centre. Another positive charge is placed outside it. The conductor is initially electrically neutral. Column I (Cause) Column II (Effect) (A) If outside charge is shifted to other position (p) Distribution of charge on inner surface of cavity changes (B) If inside charge is shifted to other position (q) Distribution of charge on outer surface of within cavity conductor changes (C) If magnitude of charge inside cavity is (r) Electric potential at the centre of conductor increased changes due to charges present on outer surface of conductor (D) If conductor is earthed (s) Force on the charge placed inside cavity changes
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- In each situation of column–I, some charge distributions are given with all details explained. The electrostatic potential energy and its nature is given situation in column–II. Column I Column II (A) A thin shell of radius a and having
a
–Q
(p)
2 0
1 Q
8 a in magnitude a charge –Q uniformly distributed
over its surface as shown
(B) A thin shell of radius 5a 2 and having (^) –Q
–Q
5a 2
(q)
2 0
3 Q
20 a in magnitude a charge –Q uniformly distributed
over its surface and a point charge
–Q placed at its centre as shown
(C) A solid sphere of radius a and having (r)
2 0
2 Q
5 a in magnitude a charge –Q uniformly distributed
–Q
a throughout its volume as shown (D) A solid sphere of radius a and having (s) Positive in sign a charge –Q uniformly distributed
–Q
a
–Q
2a
throughout its volume. The solid sphere is surrounded by a concentric thin uniformly charged spherical shell of radius 2a and carrying charge –Q as shown
ASSERTION & REASON These questions contains, Statement 1 (assertion) and Statement 2 (reason).
S t a t e m e n t – 1 : Charge is invariant. a n d S t a t e m e n t – 2 : Charge does not depends on speed or frame of reference. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement– (B) Statement–1 is True, Statement–2 is False. (C) Statement–1 is False, Statement–2 is True. (D) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–
S t a t e m e n t – 1 : Mass of ion is slightly differed from its element. a n d S t a t e m e n t – 2 : Ion is formed, when some electrons are removed or added so the mass changes (A) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement– (B) Statement–1 is True, Statement–2 is False. (C) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement– (D) Statement–1 is False, Statement–2 is True.
S t a t e m e n t – 1 : Charge is quantized a n d S t a t e m e n t – 2 : Charge, which is less than 1 C is not possible (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement– (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement– (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True.
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1 0. S t a t e m e n t – 1 : A conducting sphere charged upto 50V is placed at the centre of a conducting shell charged upto 100V and connected by a wire. All the charge of the shell flows to the sphere. a n d S t a t e m e n t – 2 : The positive charge always flows from higher to lower potential. (A) Statement–1 is True, Statement–2 is False. (B) Statement–1 is False, Statement–2 is True. (C) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement– (D) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–
1 1. S t a t e m e n t – 1 : When a charged particle is placed in the cavity in a conducting sphere, the induced charge on the outer surface of the sphere is found to be uniformly distributed. a n d S t a t e m e n t – 2 : Conducting surface is equipotential surface. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement– (B) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement– (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True.
1 2. S t a t e m e n t – 1 : Electric field intensity at surface of uniformly charge spherical shell is E. If shell is punchered at a point then intensity at punchered point become E/2. a n d S t a t e m e n t – 2 : Electric field intensity due to spherical charge distribution can be found out by using Gauss law. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement– (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement– (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True.
1 3. S t a t e m e n t – 1 : If two concentric conducting sphere which are connected by a conducting wire. No charge can exist on inner sphere. a n d S t a t e m e n t – 2 : When charge on outer sphere will exist then potential of inner shell and outer shell will be same. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement– (B) Statement–1 is True, Statement–2 is False. (C) Statement–1 is False, Statement–2 is True. (D) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement–
1 4. S t a t e m e n t – 1 : A metallic shield in form of a hollow shell may be built to block an electric field. a n d S t a t e m e n t – 2 : In a hollow spherical shield, the electric field inside it is zero at every point. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement– (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement– (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True.
1 5. Statement–1 : A hollow metallic sphere of inner radius a and outer radius b has charge q at the centre. A negatively charged particle moves from inner surface to outer surface. Then total work done will be zero. a n d S t a t e m e n t – 2 : Potential is constant inside the metallic sphere. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement– (B) Statement–1 is True, Statement–2 is False. (C) Statement–1 is False, Statement–2 is True. (D) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement–
E
NODE6 (E)\Data\2014\Kota\JEE-Advanced\SMP\Phy\Unit-07\Electrostatics\English\Exercise.p
1 6. S t a t e m e n t – 1 : Electric field E at a point P is zero if potential at that point is zero. a n d S t a t e m e n t – 2 : Potential difference between two points in space is zero if electric field at all points in space is zero. (A) Statement–1 is True, Statement–2 is True ; Statement–2 is a correct explanation for Statement– (B) Statement–1 is True, Statement–2 is True ; Statement–2 is not a correct explanation for Statement– (C) Statement–1 is True, Statement–2 is False. (D) Statement–1 is False, Statement–2 is True.
COMPREHENSION BASED QUESTIONS
Comprehension # Electrostatic force on a charged particle is given by (^) F qE
. If q is positive (^) F E
and if q negative (^) F E
. In the figure m (^) A = m (^) B = 1kg. Block A is neutral while q (^) B = –1C. Sizes of A and B are negligible. B is released from rest at a distance 1.8 m from A. Initially spring is neither compressed nor elongated.
A B
K=18N/m
smooth x=
E=10NC
x=1.8m x-axis
If collision between A and B is perfectly inelastic, what is velocity of combined mass just after collision? (A) 6m/s (B) 3m/s (C) 9m/s (D) 12m/s
Equilibrium position of the combined mass is at x = ........m.
(A)
(B) 1
(C) 5
(D) 7
- The amplitude of oscillation of the combined mass will be :–
(A)
(^2) m 3 (B)^
(^124) m 3 (C) 72 m 9 (D) 106 m 9
Comprehension # 2 A very large, charged plate floats in deep space. Due to the charge on the plate, a constant electric field E exists everywhere above the plate. An object with mass m and charge q is shot upward from the plate with a velocity v and at an angle . It follows the path shown reaching a height h and a range R. Assume the effects of gravity to be negligible.
v E
h
R
Which of the following must be true concerning the object? (A) q must be positive (B) q must be negative (C) m must be large (D) m must be small
Which of the following is true concerning all objects that follow the path shown when propelled with a velocity v at an angle ? (A) They must have the same mass (B) They must have the same charge (C) They must have the same mass and the same charge(D) Their mass to charge ratios must be the same
