Download Electromagnetics Problems: Vector Calculus, Maxwell's Equations, and Vector Fields and more Quizzes Electromagnetism and Electromagnetic Fields Theory in PDF only on Docsity!
Engineering Electromagnetics
1. An electric field on a plane is described by its potential V = 20 ( r −^1 + r −^2 ) ,
where r is the distance from the source. The field is due to a. A Monopole b. A Dipole c. Both a Monopole and a Dipole * d. A Quadruple
- The tangential component of an electric field will be continuous in which boundary? a. Conductor – Conductor b. Conductor – Dielectric c. Dielectric – Dielectric d. Any boundary *
- Magnetic vector potential is a vector …. a. Whose curl is equal to the magnetic flux density * b. Whose curl is equal to the electric field intensity c. Whose divergence is equal to electric potential d. Which is equal to the vector product E x H
4. For the wave equation E =^10 sin^ (^ ωt −^5 z^ )^ ax the wave propagation will be in
the direction of a. Y direction b. Z direction * c. X direction d. XY direction
- The electric field at a point situated at a distance d from straight charged conductor is a. proportional to d b. Inversely proportional to d * c. inversely proportional to d d. None of the above
- The intrinsic impedance of copper at high frequencies is a. Purely resistive b. Purely inductive c. Complex with a capacitive component d. Complex with an inductive component *
- “The total electric flux through any closed surface surrounding charges is equal to the amount of charge enclosed". The above statement is associated with
a. Coulomb's square law b. Gauss's law * c. Maxwell's first law d. Maxwell's second law
- Which of the following capacitors has relatively shorter shelf life? a. Mica capacitor b. Electrolytic capacitor * c. Ceramic capacitor d. Paper capacitor
9. In electromagnetics, the divergence of the magnetic field B^ is
a. Always zero b. Related to the free current density (J) * c. Always equal to the electric field (E) d. Irrelevant in electromagnetic theory
10.The circulation of the electric field (E) around a closed loop is related to: a. Magnetic flux density (B) * b. Electric potential (Φ) c. Charge density (ρ) d. None of the above
11.In vector calculus, the curl of a gradient of a scalar field is: a. Always zero * b. Always a scalar c. Always a vector d. None of the above
12.Stokes' theorem is used to relate: a. Flux and charge b. Surface integrals and volume integrals * c. Divergence and curl d. Electric and magnetic fields
13.In Maxwell's equations, the term ∇×E is associated with a. Magnetic monopoles b. Magnetic flux density (B) * c. Electric charges d. Charge Density (ρ)
b. The circulation of the vector field F along the curve C * c. The flux of the vector field F through the curve C d. The potential of the vector field F along the curve C
- The line integral (^) ∫ c
f ( x , y ) ds represents the integral of a scaler field f ( x , y ) along
a curve C and is also known as a. A path integral * b. A surface integral c. A volume integral d. A flux integral
- Green's theorem relates a line integral along a closed curve to: a. A surface integral over a closed surface b. A surface integral over a simple closed curve c. A double integral over a closed region in the plan * d. A volume integral over a solid region
- Evaluate (^) ∫ c
( y ¿¿ 2 i + 2 x j ). dr ¿ along the curve C from (1,0) to (3,4)
a. 19 * b. 20 c. 21 d. 22
- Compute the line integral (^) ∫ c
2 x i − y j ¿. dr ¿ over the curve C from (0,0) to (1,2)
a. 1 b. 2 * c. 3 d. 5
- Identify which one of the following is not an electromagnetic wave
a. 50 e −^ j^ ( ωt −^3 z^ )
b. sin( ω ( 10 z + 5 t ))
c. cos ( y^2 + 5 t ) *
d. sin x cos t
- When two vectors are perpendicular, their a. Dot product is zero * b. Cross product is zero c. Both are zero
d. Both are not necessarily zero
- Which of the following is not a vector function in Electromagnetics? a. Gradient b. Divergence c. Electric potential * d. Curl
- For the point P (3,60°,2) in cylindrical coordinates and the potential field V = 10(ρ +1)z^2 cosφ V in free space, find at P, the value for V a. 60v b. 80v * c. 100v d. 220v
- What primarily determines the capacitance per unit length of a two-wire transmission line? a. Wire length b. Wire separation * c. Wire material d. Wire diameter
- Increasing the separation between the wires in a two-wire transmission line will result in: a. Increased capacitance * b. Decreased capacitance c. No change in capacitance d. Increased inductance
- For a two-wire transmission line with a wire separation d of 3 mm and wire radius a, of 1.5 mm, calculate the wire-to-wire capacitance for a length of 5 meters.
(Given: ε r = 2 ∧ εo =8.85 × 10 −^12 F / m )
a. 3.54×10-11^ F b. 1.77×10-10^ F * c. 3.54×10−10^ F d. 1.77×10−11^ F
- Calculate the capacitance per meter length of a two-wire transmission line with wire separation d of 6 mm and a relative permittivity εr of 3. The wires have a radius of 2.5 mm each. (Given: Vacuum permittivity, ε 0 =8.85×10−12^ F/m) a. 7.07×10−11^ F/m b. 3.54×10−11^ F/m *
c. 14 CV^^2 *
d. 18 CV^^2
- The electric potential due to an infinite plane sheet of charge with surface charge density σ at a distance r from it in free space is given by:
a. 2 σ ε 0
b. σ ε 0 *
c. 4 σ ε 0
d. 2 ε^ σ 0
In a steady-state magnetic field, the term "magnetic flux" through a surface is calculated as the: a. Integral of the magnetic field strength over the surface b. Product of magnetic field strength and surface area * c. Integral of the magnetic field strength perpendicular to the surface d. Product of magnetic field strength and the angle between the field and surface
When a conductor carries a current and is placed in a steady magnetic field, the force experienced by the conductor is governed by: a. Ampere's law b. Ohm's law c. Faraday's law d. Lorentz force law *
According to Ampere's law in integral form, the line integral of the magnetic field B around a closed path C is equal to: a. The total magnetic flux through any surface bounded by C b. The current enclosed by the path C * c. The rate of change of electric field through the path C d. The rate of change of magnetic field through the path C
Which of the following statements best describes the behavior of a magnetic material in a steady magnetic field? a. It exhibits permanent magnetization * b. Its magnetic properties change constantly c. It becomes an ideal diamagnetic material d. It shows a constant increase in susceptibility
- According to Maxwell's equations, in a steady magnetic field, what is the mathematical expression for the divergence of the magnetic flux density B?
a. ∇. B = 0 *
b. ∇^.^ B = μ 0 ρ
c. ∇^.^ B =^ ∂ ∂^ ρt
d. ∇^.^ B = μ 0 J
When determining the magnetic field due to steady currents using the Biot- Savart law, what is the relationship between the differential current element and the resultant magnetic field? a. Inversely proportional b. Directly proportional * c. Independent d. Non-linear
Calculate the magnetic field (B) at a distance of 4 cm from a long straight wire carrying a current of 5 A. (Given: Permeability of free space, μ 0 =4π×10−7^ T⋅m/A) a. 1.26×10−6^ T b. 2.00×10−6^ T c. 5.00×10−6^ T d. 2.51×10−5^ T *
In electromagnetism, the curl of the magnetic field B is used to express: a. Ampere's law * b. Gauss's law c. Faraday's law d. Ohm's law
In the context of electromagnetic induction, the curl of the induced electric field E is related to: a. Changing magnetic flux * b. Electric potential difference c. Charge distribution d. Magnetic permeability
Calculate ∇×F for F = (3xz+y2) i+(2xy−z2) j+(x2−2yz) k. a. −2i+2xj+3k * b. 2i−2xj−3k c. −2i+2xj−3k d. 2i−2xj+3k
a. ∮ C E ⋅ d l = −
d ΦB
dt *
b. ∮ C H ⋅ d l = ∬ S ∇× E ⋅ d a c. ∮ C D ⋅ d l = ∬ S ρ ⋅ d a d. ∮ C B ⋅ d l = μ 0 ∬ S J ⋅ d a
- In wave propagation through a medium, the ratio of the electric field strength to the magnetic field strength is represented by: a. Permeability b. Impedance * c. Conductivity d. Permittivity
- Compute the cross product, A x B of the vector fields A=3 i−2 j+4 k and B=i + 5 j −2 k? a. 14i−11j−13k b. 14i−13j−11k * c. −14i−11j−13k d. −14i−13j−11k
- If A ⋅ B = 0, what can be said about the angle between vector fields A and B? a. They are perpendicular * b. They are collinear c. They are anti-parallel d. They are at a right angle
- The scalar triple product of three vector fields A, B, and C is zero. What does this imply? a. A, B, and C are coplanar * b. A, B, and C are perpendicular c. A, B, and C are parallel d. A, B, and C are orthogonal
- For vectors A =2 i −3 j +4 k and B = i +2 j − k , what is ∣ A × B ∣?
a. 66
b. (^) √ 29 *****
c. 5
d. (^) √ 21
- Using concepts from Stokes’ theorem, calculate the circulation of the vector field F=(x2+y) i+(y2−z) j+(xz−y2) k around the closed curve C that is the intersection of the plane z=2 and the cylinder x^2 +y^2 =4 oriented counterclockwise when viewed from above the xy - plane.
a. 16π * b. −16π c. 8π d. −8π
- Dielectric strength ______ with increasing thickness a. Increases b. Decreases * c. remains unaltered d. none of the above
- The property of a capacitor to store electricity is called its a. capacitance * b. charge c. energy d. none of the above
- In the left hand rule, forefinger always represents a. Voltage b. Current c. magnetic field * d. direction of force on the conductor
- The depth of penetration of a wave in a lossy dielectric increases with increasing a. Conductivity b. Permeability c. Wavelength * d. Permittivity
- Given a particle at a point C(−3, 2, 1) , compute it’s spherical coordinates a. C(r = 3.74, θ = 74.5^0 , φ = 146.3^0 ) * b. C(r = 5.74, θ = 90^0 , φ = 146.3^0 ) c. C(r = 5.74, θ = 90^0 , φ = 180^0 ) d. C(r = 3.74, θ = 74.5^0 , φ = 90^0 )
- Given a particle at a point D(r = 5, θ = 20◦, φ = − 70^0 ), compute its rectangular coordinates a. D(x = 0.685, y = −1.607, z = 4.70) b. D(x = 0.585, y = −1.607, z = 4.70) * c. D(x = 0.985, y = −1.607, z = 4.70) d. D(x = 0.485, y = −1.607, z = 4.70)
d. -66.5az
- A conducting sheet with a surface charge density of 7×10−6^ C/m^2 generates what electric field intensity 3m away from the sheet? a. 2.33×10^5 N/C * b. 1.4×10^5 N/C c. 4.67×10^5 N/C d. 7×10^4 N/C
- What does electric flux density (D) represent in electrostatics? a. Electric field strength in a material medium * b. Electric field intensity in a vacuum c. Electric field lines passing through a surface d. Electric field potential difference
- Electric flux density (D) is related to electric field intensity (E) and permittivity (ϵ) of the material by which equation? a. D = ϵE * b. E = ϵD c. D = ϵE
d. E = D ϵ
- In what units is electric flux density (D) measured? a. Newton per coulomb (N/C) b. Coulomb per square meter (C/m^2 ) * c. Volt per meter (V/m) d. Farad per meter (F/m)
- For a material with a permittivity of 6×10−9^ F/m and an electric field intensity of 200V/m, what is the electric flux density (D)? a. 1200C/m^2 b. 1.2×10−5C/m^2 * c. 33.33C/m^2 d. 1.2×107C/m^2
- Which of the following statements about electric flux density (D) is true? a. It is always greater than the electric field intensity (E) b. It represents the total electric field passing through a surface c. It is constant for all materials
d. It depends on the material and the electric field passing through it *
- Gauss's Law in differential form states that the divergence of the electric flux density (∇⋅D) within a differential volume element (δV) is equal to: a. The total charge enclosed by the volume element divided by the permittivity of free space (ϵ 0 ) * b. The total charge enclosed by the volume element c. The electric field intensity (E) multiplied by the total charge enclosed by the volume element d. Zero
- What does a differential volume element signify in Gauss's Law applications? a. It represents an infinitesimal portion of the total volume under consideration b. It depicts the entire enclosed volume within a surface c. It defines the magnitude of the electric field at a point within a volume d. It indicates the divergence of the electric field intensity
- If a differential volume element encloses a charge of 5 ×10−6C and the permittivity of free space is 8.85×10−12^ F/m, what is the divergence of the electric flux density (∇⋅D) within this volume element? a. 5×10−6F/m^2 * b. 56.5×10−6F/m^2 c. 565×10−6F/m^2 d. 5650×10−6F/m^2
83. Find div D at the origin if D = e − x^ sin y ax − e −^ x^ cos y a y + 2 z az
a. 5 b. 3 c. 2 *
d. ∞
- Calculate the work done in moving a 4-C charge from B(1, 0, 0) to A(0, 2, 0) along the path y = 2 − 2x, z = 0 in the field E = 5ax V/m a. 22J b. 20J * c. 25J d. 28J
- Calculate the work done in moving a 4-C charge from B(1, 0, 0) to A(0, 2, 0) along the path y = 2 − 2x, z = 0 in the field E = 5x ax + 5y ay V/m a. -20 J b. 20 J c. -30 J *
- Which antenna type produces radiation in all directions with equal power and phase, often used in radio broadcasting? a. Dipole antenna b. Yagi-Uda antenna c. Isotropic antenna d. Parabolic antenna
- In the context of antennas, what does the term "gain" refer to? a. The ratio of the maximum radiation intensity in the desired direction to that of an isotropic antenna * b. The ratio of the signal strength to noise c. The ability of an antenna to focus electromagnetic energy d. The wavelength of the electromagnetic wave
- The orthogonal trajectory of the family of curves x^2 −y^2 =c, where c is a constant is given by: a. x^2 + y^2 = c * b. x y = c c. x^2 − y^2 = −c d. x^2 + y^2 = −c
- Applying Green's theorem to ∮C (x^2 +y^2 )dx+(2xy)dy, where C is the boundary of the region enclosed by the parabola y=x^2 and the line y=x from the point (0,0) to (1,1), yields:
a. 13
b. 12
c. 23
d. 0 *
- The Laplacian operator …….. a. Is a scalar function b. Is a vector function c. Can be a scalar or vector function * d. None of the above
- In cylindrical coordinates system, z ranges from … a. 0 and 1 b. -∞ and 0
c. 0 and -∞ d. -∞ and ∞ *
- Tesla is the unit of which quantity? a. Field strength b. Inductance c. Flux density * d. Flux
- Which of the following rays are not electromagnetic waves? a. Gamma rays b. Beta rays * c. Heat rays d. X rays
- The curl of the gradient of a scalar function f is always zero in three- dimensional Cartesian coordinates. Which of the following expressions correctly demonstrates the result of the proof? a. ∇ × ( ∇ f ) = 0 * b. ∇ × ( ∇ f ) = ∇ ⋅ ∇ f c. ∇ × ( ∇ f ) = ∇ f d. ∇ × ( ∇ f ) = ∇ ⋅ 0
