# Objective Questions or MCQ on Electromagnetic Theory Page – 7

1. An electrick field on a place described by its potential
V = 20(r-1 + r - 2 ) where r is the distance from the source. The field is due to

For a monopole, electric field varies inversely with r2 while its potentila varias inversely with r. Similary for a dipole its electric field varias inversely as r3 and potential varias as r2. In the given expression on both terms are present, so this potential is due to both monopole and dipole.

2. Two point charges are in the vertex of the square. If potential is another vertex is 2 V, so potential is opposite vertex (diagonally) is

Plane between midway θ and θ i.e one passing through ABC and perpendicular to plane of paper is another equipotential. Hence potential at C = potential at A = 2 V.

3. A parallel plate capacitor with air as dielectric, force between plate is F. If capacitor is now immersed water of dielectric εr, force between plate will be –

$\frac{E_1}{E_2} \; = \; \frac{\epsilon _r}{1}$
$F_2= \frac{1}{2} \epsilon_0 \epsilon_r E_2^2$.

4. Inside a hollow conducting sphere

For any point on any concentric sphere inside the conducting sphere, the charge enclosed by the concentric sphere is zero and hence electric field is zero.

5. Two identical circular coils, one closed and another is little split (not enclosed) are placed in an uniform magnetic field which decrease at a constant rate. If the plane to the coils are perpendicular to the field which of the following statements is true?

Whenever a coil open or closed, cuts magnetic line of force, an emp is induced in it.

6. A long wire composed of a smooth round conductor runs above and parallel to the ground (assumed to be a large conducting plane). A high voltage exits between the conductor and the ground. The maximum electric stress occur at

Since the distance from ground to lower surface is less than from ground to upper surface. So electric stress is maximum at lower surface.

7. A loop is rotating about x-axis in a magnetic field, B = BO cos(ω + φ) ay. The voltage in the loop is

Whenever a moving circuit is kept in a time varying magnetic field induce emf have two components. One for time variation of B and other for turn motion of circuit in B.

8. If c1 = 8 μF, c2 = 4 μF, c3 = 7 μF c1, c2 are in servies with c3; effective capacitance will be

c1 + c2 = 8+4 = 12 μF
ceq = (12 × 7) / (12+7) = 4.42 μF.

9. A metal sphere with 1 m radius and a surface charge density of 10 coulombs / m2 is enclosed in a cube of 10 m side. The toatal outward electric displacement normal to the surface of the cube is.

D = q × 4π r2.

10. An electric dipole of moment P is placed in front of a ground sphere. The change induced on the surface of the sphere is (Assume radius of sphere = R and distance from dipole to centre of sphere = d)

Charge induced on a spherical surface = - QR/D
Whwre Q = inducing point charge
D = distance of the point charge from the centre of sphere.
Total charge induce in present case,
$Q= \; - qr \left [ \frac{1}{d+D/2} - \frac{1}{d-D/2} \right ] = \frac{- qD.R}{d^2 – (D^2)/4}$
Now for a dipole D is very small i.e. D << d
Hence Q = PR/d2 where, P = qD, the dipole moment.

11. What is the value of total electric flux coming out of a closed surface?

According to gauss theorem, the total electric flux through any closed surface surrounding charges is equal to the amount to charges enclosed by the surface.

12. Electric field strength of charge

Electric field strength or electric field intensity.
$E = \frac{Q}{4 \pi \epsilon d^2}$.

13. A capacitor having a mica dielectric εR = 6, a plate area of a 10 inches2 and a separation 0.01 inch. Find the value of C

s = 10 × (0.0254)2
d = 0.1 × (0.0254)
c = εR s/d.

14. The statement which is not correct from the following:

It is E = ρL/(2πε0.r).

15. Two infinite parallel metal plates are charged with equal surface charge density of the same plates is.

For an infinite sheet of charge having surface charge density ρs, the electric field on either side is ρ/2ε and away from it assuming charge to be the positive). Therefore, in the region between the plates, the two fields are anti parallel and equal.

16. Two point charges 4μc are placed at a distance of 3 cm apart from each other in free space. Force acting on two charges will be

Use coulomb’s law.

17. An insulated metal sphere of 20 cm diameter is charged by rubbing with charges 2 × 10-8 C. Potential developed will be

$V = \frac{q}{4 \pi \epsilon_0 r}$.

18. An electric field of 1.92 × 103 N/c is maintained across two plates separated 0.015 m. Potential difference across plates will be

V = E.d.

19. Which of the following statement are incorrect?

E is normal to conductor.

20. Between a hollow and solid metal sphere, charge reside

Charge always reside outer surface of any object.