Solved Example: 9994-01

The electric field strength at distant point, P, due to a point charge, +q, located at the origin, is 100 $\mu$ V/m. If the point charge is now enclosed by a perfectly conducting metal sheet sphere whose center is at the origin, then the electric field strength at the point, P, outside the sphere, becomes: (GATE ECE 1995)

A. Zero

B. 100 $\mu$ V/m

C. – 100 $\mu$ V/m

D. 50 $\mu$ V/m

The point charge +q will induce a charge – q on the surface of metal sheet sphere. Using Gauss’s law, the net electric fulx passing through a closed surface is equal to the charge enclosed = + q – q = 0 D = 0, E = 0 at point P.

Correct Answer: A

Solved Example: 9994-02

A metal sphere with 1 m radius and surface charge density of 10 Coulombs / m$^2$ is enclosed in a cube of 10 m side. The total outward electric displacement normal to the surface of the cube is: (GATE ECE 1996)

A. 40 $\pi$ Coulombs

B. 10 $\pi$ Coulombs

C. 5 $\pi$ Coulombs

D. None of the above

The sphere is enclosed in a cube of side = 10m. using Gauss’s law, the net electric flux flowing out through a closed surface is equal to charge enclosed. \[\begin{aligned} \iint_s \bar(D) \cdot \bar{da} &= Q (enclosed)\\ &= P_S 4 \pi r^2\\ &= 10 \times 4 \pi\\ &= 40 \pi Coulombs\end{aligned}\]

Correct Answer: A

Solved Example: 9994-03

The thumb in Fleming's left hand rule indicate: (UP Jal Nigam E&M 2016)

A. Motion

B. Current

C. Field

D. None from the above

Correct Answer: A

Solved Example: 9994-04

Electric flux is a _______ field, and its density is a _______ field. (NLC GET ECE Nov 2020)

A. Vector, vector

B. Scalar, vector

C. Vector, scalar

D. Scalar, scalar

Correct Answer: B

Solved Example: 9994-05

Find H = ___________ A/m at the center of a circular coil of diameter 1 m and carrying a current of 2 A. (SSC JE EE Sep 2019 Morning)

A. 0.6366

B. 0.1636

C. 6.366

D. 2

Correct Answer: D

Solved Example: 9994-06

The force between two charges is 200 N. If the distance between the charges is doubled, the force will be _______. (DFCCIL Jr. Executive S and T Sep 2021)

A. 400 N

B. 100 N

C. 50 N

D. 200 N

Correct Answer: C

Solved Example: 9149-01

The divergence theorem converts:

A. Line to surface integral

B. Surface to volume integral

C. Volume to line integral

D. Surface to line integral

Correct Answer: B

Solved Example: 9149-02

Evaluate Gauss law for D = 5r$^2$/4 i in spherical coordinates with r = 4m and $\theta$ = $\dfrac{\pi}{2}$ as volume integral.

A. 600

B. 588.9

C. 577.8

D. 599.7

Correct Answer: B