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Right choice is (B) 1.12

For explanation I would say: The electric field due to plate of charge will be E = ρs/2εo. Put ρs = 20, we get E = 20/(2 X 8.854 x 10^-12) = 1.129 x 10^12 UNITS.

Right option is (d) Triangle

The explanation: When any field or potential needs to be CALCULATED for either line charge or coaxial CABLE or concentric cylinder, the method of IMAGES uses a triangle which CONVERTS the three dimensional problem to one dimensional analysis. From this, the result can be calculated.

Right choice is (c) Zero RESISTANCE

Explanation: Since RESISTIVITY is directly proportional to the resistance, when the resistivity is zero, resistance is also zero. THUS we get zero resistance. The option infinite conductance is also possible ideally, but it is not possible PRACTICALLY. As there is always some loss in the FORM of heat, thus infinite conductance is impossible, but a short circuit (zero resistance) is practically possible.

Right answer is (b) 0.5

The best I can explain: The dissipation factor is nothing but the TANGENT of LOSS ANGLE of loss tangent. Tan δ = Series RESISTANCE/Capacitive resistance = 5/10 = 0.5.

The correct option is (B) 12

To explain I would say: The ELECTRIC field intensity is given by the ratio of POTENTIAL to distance or length. E = V/d = 24/2 = 12 V/m.

Right OPTION is (b) 2.33 kohm

The EXPLANATION is: POTENTIAL is GIVEN by V = Q/C. PUT Q = 28C and C = 12 mF. We get V = 28/12 x 10^-3 = 2.333 x 10^3 ohm.

The correct answer is (a) Easy approach

For explanation I would SAY: Electrostatic BOUNDARY value problems are difficult if Poisson and Laplace equation is solved directly. But method of images helps us to solve problems without the equations. This is done by replacing boundary surfaces with APPROPRIATE IMAGE CHARGES.

Correct OPTION is (b) 88.4

The EXPLANATION is: Capacitance is given by, C = εo A/d. PUT A = 2, d = 0.2, εo = 8.854 x 10^-12, we get C = 8.841 x 10^-11 = 88. 41 pF.

The correct choice is (B) 0.222 nF

The explanation is: The concentric shell with infinite outer radius is considered to be an isolated sphere. The CAPACITANCE C = 4πε/(1/a – 1/b). If b->∞, then C = 4πεa. PUT a = 2m, we GET C = 4π X 8.854 x 10^-12 x 2 = 0.222 nF.

Correct answer is (d) 0.5

Explanation: The time constant for an R-L series CIRCUIT will be τ = L/R. Put R = 4 and L = 2. We GET τ = 2/4 = 0.5 second.

The correct ANSWER is (b) OPEN path

For EXPLANATION: When there exists infinite resistance in a path, the current flowing will ideally be zero. This is POSSIBLE only for an open path/circuit.

The correct answer is (a) 37 kohm

To EXPLAIN I would SAY: Orange refers to number 3. Violet refers to number 7. The third COLOUR code orange refers to 103. Thus the resistor VALUE will be 37 kilo ohm.

Correct OPTION is (a) -20 i – j

The explanation: The electric field is given by E = -Grad(V). The gradient of the given function is 20I/x + j. At the point (1,1,0), we GET 20i + j. The electric field E = -(20i + j) = -20i – j.

Correct ANSWER is (C) 5

For explanation I would say: From point form of Gauss law, we GET Div (D) = ρv

Div (D) = Div(12x – 7Z) = 12-7 = 5, which the charge DENSITY ρv. Thus ρv = 5 units.

The correct option is (a) POINT form of GAUSS LAW

The best I can EXPLAIN: The point of Gauss law is given by, Div (D)= ρv. On putting

D= ε E and E=- Grad (V) in Gauss law, we get Del^2 (V)= -ρ/ε, which is the Poisson equation.

Correct choice is (a) 1/6π

Best explanation: The Poisson equation is given by Del^2(V) = -ρ/ε. To find ρ, put ε = 8.854 x 10^-12 in air and LAPLACIAN of the function is 2 + 2 + 2 = 6. Ρ = 6 x 10^-9/36π = 1/6π UNITS.

The CORRECT choice is (a) Laplace equation

The best EXPLANATION: Step is a CONSTANT FUNCTION. The Laplace equation Div(Grad(step)) will become ZERO. This is because gradient of a constant is zero and divergence of zero vector will be zero.

Correct answer is (b) CURRENT will be infinite

For explanation I WOULD SAY: Laplace equation satisfying implies the potential is not necessarily ZERO DUE to subsequent gradient and divergence operations following. Finally, if potential is assumed to be zero, then resistance is zero and current will be infinite.

The correct choice is (c) LAPLACE equation

To explain I would SAY: The POISSON equation is GIVEN by Del^2(V) = -ρ/ε. In free space, the charges will be zero. Thus the equation BECOMES, Del^2(V) = 0, which is the Laplace equation.

The correct choice is (a) V = x^2 + y^2 – z^2. State True/False.

To explain I would say: Grad (V) = 2xi + 2yj – 4zk. DIV (Grad (V)) = Del^2(V) = 2+2-4 = 0. It satisfies the LAPLACIAN equation. THUS the STATEMENT is true.