Download Point Charges - General Physics - Solved Exam and more Exams Physics in PDF only on Docsity! Q.L. A point charge Q:= 49.0 nC is placed at the origin of an xy-coordinate system. Another
point charge Q, =—100 nC is placed on the positive x-axis at x = 7.0 cm and a third point
charge Q; = 225 nC is placed at the point x = 16 em, y = 12 em.
@) a) Show these point charges on the given coordinate system.
mw Yelemy — - -- £&,
© 40 80 1% «NRO y fem)
© b) Find the farce acting on the charge Q2 due to the charge Q;. Give it in unit vector notation.
F,ak Qo, Fon tox ayo (loa) o>
ak 2S ae Se ae
¥
Ke (onts®)*
== %Ox1s Nh
@.. * F< Fo. rN
@ ¢) Find the force acting on the charge Q) due to the charge Qs. Give it in unit vector notation,
Sake Fa = qoxts? contd "a(2is 5? ge oy
ie [qeasoyty 42"sa" (Bt eiagy ts
; .
a= =o 2238 _ ys? a -%ox\e N
Las .
2esxia?
Ge =
, 5
Bae 4i saa py N
@) d) Find the net force mane on the charge Q; . Give it in unit vector notation.
a3 7 Ped va.
= VOX % O16 U4 4,0 510 *O,% | hi
B= (ats)? Nw
2
B= Fat Ge a=Laots (atste yf? nv
cr 316 aw
R= =t 1 Ve hePy re N
Fa Cx tayo
Q.2. A non-conducting sphere with radius R has a spherically symmetric charge distribution
of volume charge density p(r) = po (1 -1/2R), where p, is a positive constant.
a) Obtain an equation for the electric field (in terms of p,,8o,R and r) for the points inside
the sphere, where r< R.
Tenet. = Vsdy =s§li~ 2) Amytdr = =ans, (15 - aE )
EKG) = HKS.0F (-e - dy) /So
E= 8.0 (8R-Zr)/24RE, Fat (8R-Sr)/2hRe
06 b) Obtain an equation for the electric field ( in terms of p,.6).R and r) for the points
outside the sphere, where r>R.
cS
R
= = Reo Ri ys
Fenel, = Ssdv SANS aR J=Z HR
E (ater) = 2AGR'/E.
— 5 oR? TF
Fas fk Ey 58R/24E. r?
oz 9 Show that the equations of part a and b yield the same result for the points on the
surface of the sphere, where r= R,
at YroaR oan
Fiom part a) = SR (BR-SR)/ BOR = SER /24G
From part b) Ex 58R/2HER® = SSR/NG
E, = Fy 58R/26
O 4 d) If the total charge in the sphere is Q, determine the constant p, (in terms of Q and R),
From part b, the total charge ow the sphere
is 3 Hence
Z m3, rR?
gatas? s 8 =6a/srr $= SQ/5R*
