Electrostatics and Magnetostatics
Spatial Relationships
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
Vector Analysis
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