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The CORRECT answer is (c) H = -GRAD(V)

The best I can explain: For any magnetic FIELD, the magnetic field intensity will be the negative gradient of the potential of the field. This is given by H = -Grad(V).

Correct answer is (d) B = μ H

To explain I would say: The magnetic flux density is the product the PERMEABILITY and the magnetic FIELD INTENSITY. This STATEMENT is always true for any MATERIAL (permeability).

Right choice is (C) A

To ELABORATE: The Maxwell equations can be used to compute E,H,D,B and J DIRECTLY. It is not possible to FIND the magnetic vector POTENTIAL A directly.

Correct answer is (a) 14.06

Easiest EXPLANATION: The magnetic energy possessed by a COIL is given by E = 0.5 x LI^2. PUT L = 18 x 10^-3 and I = 1.25, thus we get E = 0.5 x 18 x 10^-3 x 1.25^2 = 14.06 x 10^-3 UNITS.

The correct OPTION is (a) 15.6mH

To EXPLAIN I would say: The energy stored in an inductor is GIVEN by E = 0.5 LI^2. To get L, PUT E = 2 and I = 16 and thus L = 2E/I^2 = 2 X 2/16^2 = 15.6mH.

The correct option is (c) INDUCTANCE

Explanation: The magnetostatics highly relies on the inductance of the MAGNETIC materials, which decides its BEHAVIOR in the INFLUENCE of magnetic field.

The correct answer is (b) Emf generated by ENERGISING the coil

To ELABORATE: The inductance is a property of an electric conductor/coil which measures the amount of emf generated by PASSING CURRENT through the coil.

The CORRECT OPTION is (a) 25.31

Explanation: The energy stored in an inductor is given by E = 0.5 LI^2. Thus, put L = 5 and I = 4.5 and we GET E = 0.5 x 5 x 4.5^2 = 50.625 UNITS To get power P = E/t = 50.625/2 = 25.31 units.

The correct choice is (c) 498

The BEST I can explain: The inductance of any MATERIAL(coil) is given by L = μ N^2A/I.

Put L = 23.4 x 10^-3, I = 2 and A = 0.15, we get N as 498 turns.

Correct answer is (a) 4.07

To explain I would say: The magnetic energy is given by E = 0.5 μ H^2 and we know that μH = B. On substituting we GET a FORMULA E = 0.5 B^2/μ. Put B = 32 and in AIR μ = 4π x 10^-7, we get E = 0.5 x 32^2/4π x 10^-7 = 4.07 x 10^8 units.

The correct choice is (a) 0.75mH

To EXPLAIN: The inductance of any MATERIAL(coil) is given by L = μ N^2A/I. On substituting N = 100, A = 0.12 and I = 2, we get L = 4π X 10^-7 x 100^2 x 0.12/2 = 0.75 units.

The CORRECT option is (a) 1.26

Easiest explanation: The MAGNETIC ENERGY is given by E = 0.5 μ H^2. PUT H = 14.2 and in air μ = 4π x 10^-7, we get E = 0.5 x 4π x 10^-7 x 14.2^2 = 1.26 x 10^-4 UNITS.

Right choice is (b) 128

Explanation: The WORK done in the INDUCTOR will be W = 0.5 x LI^2. On substituting L = 4 and I = 8, we get, W = 0.5 x 4 x 8^2 = 128 units.

The correct option is (B) -4

The best I can EXPLAIN: The induced EMF is given by e = -Ldi/dt. PUT L = 2 x 10^-3 and di/dt = 2000 in the equation. We get e = -2 x 10^-3 x 2000 = -4 units.

Correct ANSWER is (c) K dS

The best I can explain: The magnetic vector POTENTIAL for the surface INTEGRAL is GIVEN by A = ∫ μKdS/4πR. It is clear that the CURRENT element is K dS.

Correct answer is (d) R

Explanation: The magnetic VECTOR potential for the LINE INTEGRAL will be A = ∫ μIdL/4πR. It is clear that the potential is INVERSELY proportional to the distance or radius R.

The correct option is (B) -12π x 10^-7

For explanation I would say: The field intensity H = -GRAD(V). Since the given potential is a position vector, the gradient will be 3 and H = -3. Thus the flux DENSITY B = μH = 4π x 10^-7 x (-3) = -12π x 10^-7 units.

The CORRECT OPTION is (a) –μ J

To explain: The Laplacian of the MAGNETIC vector potential is given by Del^2(A) = -μ J, where μ is the permeability and J is the CURRENT DENSITY.

Right answer is (b) -20

The EXPLANATION is: The FIELD intensity H = -GRAD(V). To get V, integrate H with respect to the variable. Thus V = -∫H.dl = -∫60x^2 DX = -20x^3 as x = 0->1 to get -20.

The CORRECT CHOICE is (c) 12

Explanation: The field intensity is given by H = – Grad(V). The gradient is given by 0 – 12cos y. At the origin, the gradient will be -12 cos 0 = -12. Thus the field intensity will be 12 units.

Correct choice is (b) I

The explanation is: By Stoke’s theorem, ∫ H.dL = ∫ CURL(H).dS and from Ampere’s law, Curl(H) = J. Thus ∫ H.dL = ∫ J.dS which is nothing but CURRENT I.

The correct choice is (b) -6

Easiest explanation: The magnetic FIELD intensity is given by H = -GRAD(Vm). The gradient of Vm is 1 + 2 + 3 = 6. Thus H = -6 units.

Correct OPTION is (b) False

Explanation: The magnetic vector POTENTIAL could be learnt as a scalar. But it is ACTUALLY a vector quantity, which means it has both magnitude and DIRECTION.

Right option is (b) -∫(4sin z i – ex J – 3cos y k)dt

The explanation is: We know that Curl (E) = -dB/dt. The curl of E is (4sin z i – ex j – 3cos y k). To GET B, integrate the -curl(E) with respect to TIME to get B = -∫(4sin z i – ex j – 3cos y k)dt.

The correct answer is (B) 186.67

To explain I WOULD SAY: The total flux is the product of the magnetic flux density and the area. Total flux = B x A. To GET B, put flux/area. B = 28/0.15 = 186.67 units.

Right choice is (c) H = -GRAD(Vm)

The EXPLANATION is: The given CONDITION shows that the magnetic field intensity will be the NEGATIVE gradient of the magnetic vector potential.

Right option is (b) –i – j – k

For explanation I WOULD say: The magnetic flux density is the curl of the magnetic vector POTENTIAL. B = Curl(A). THUS Curl(A) = i(-1) – j(1) + k(-1) = -i – j – k. We get B = -i – j – k.

Right answer is (a) 6.36

The explanation: We how that, B = μH. To get H = B/μ, PUT B = 8 X 10^-6 and μ = 4π x 10^-7. Thus H = 8 x 10^-6/ 4π x 10^-7 = 6.36 units.

Right answer is (B) 1

Best explanation: From Ampere law, we GET ∫ H.dL = I. Put H = 2L and L = 0->1. On integrating H with respect to L, the current will be 1A.

The correct option is (a) 23.4

The best EXPLANATION: The TOTAL FLUX is given by φ = ∫ B.ds, where ∫ds is the area. Thus φ = BA. We get φ = 11.7 x 2 = 23.4 units.

Correct CHOICE is (d) 0

To explain: We KNOW that the divergence of B is zero. Also B = μH. THUS divergence of H is also zero.

Correct OPTION is (a) 103.45

To explain: The MAGNETIC FIELD intensity of a toroid is given by H = NI/2πrm. Put N = 40, I = 3.25 and RM = 0.2, we get H = 40 x 3.25/2π x 0.2 = 103.45 units.

Correct answer is (C) Tesla

The BEST explanation: The unit of MAGNETIC flux density is weber/m^2. It is ALSO called as tesla.

The correct choice is (c) 0

For explanation: The inner radius is 1.5cm and the outer radius is 4cm. It is clear that the magnetic field intensity NEEDS to be CALCULATED outside of the conductor ie, r>4cm. This will lead to zero, SINCE H outside the conductor will be zero.

Right choice is (b) 2

The explanation: The MAGNETIC FIELD intensity of an INFINITELY long conductor is given by H = I/2πh. Put I = 6.28 and H = 0.5, we get h = 1/0.5 = 2 units.

Right CHOICE is (a) 8π x 10^-7 cos t

The BEST I can explain: Given H = 2sin t. We GET B = μH = 4π x 10^-7 x 2sin t = 8πx10^-7sin t.

To get E, integrate B with respect to time, we get 8πx10^-7cos t.

Right ANSWER is (b) 3

Easy explanation: We know that B = μH. On SUBSTITUTING μ = 4π X 10^-7 and H = 2.4, we get B = 4π x 10^-7 x 2.4 = 3 x 10^-6 UNITS.

The correct option is (d) Curl of H is same as the current density

For explanation: Ampere circuital law or Ampere law states that the closed integral of the MAGNETIC FIELD INTENSITY is same as the current enclosed by it. It is given by Curl(H) = J.

Correct answer is (a) True

Explanation: The MAGNETIC FIELD intensity is directly proportional to the magnetic field intensity for a PARTICULAR material (Permeability). It is given by B = μH.

Right ANSWER is (b) Displacement CURRENT

To explain I would SAY: The charge in the CAPACITOR is due to displacement current. It is the current in the presence of the dielectric placed between two parallel metal plates.

The correct option is (a) Static

Explanation: MAXWELL equations can be represented in differential/point form and integral form alternatively. SOMETIMES, it can be represented by time varying fields called HARMONIC form.

Correct choice is (a) Transformer EMF

The BEST I can explain: The stationary loop in a varying magnetic field results in an induced emf DUE to the change in the flux LINKAGE of the loop. This emf is called as induced or transformer EMF.