Electromagnetic theory miscellaneous

Electromagnetic theory miscellaneous

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Electromagnetic Theory

Electromagnetic theory miscellaneous
  1. The energy stored in the magnetic field of a solenoid 30 cm long and 3 cm diameter wound with 1000 turns of wire carrying a current of 10 A is—








  1. View Hint View Answer Discuss in Forum

    Since we know that,
    L = N2 × ρ
    given
    N = 1000 turns diameter
    = 3 cm, L = 30 cm.

    ρ =
    µ0A
    		 =
    4π × 10–7 × π × (1.5 × 10–2)2
    L0.3

    = 29.6088 × 10–10
    L = 29.6088 × 10–10 × (103)2
    = 29.6088 × 10–4 H
    where,
    L = length of solenoid
    W = 1/2 LI2
    = 1/2 × 29.6088 × 10–4 × (10)2
    = 0.148 ≈ 0.15 J.

    Correct Option: B

    Since we know that,
    L = N2 × ρ
    given
    N = 1000 turns diameter
    = 3 cm, L = 30 cm.

    ρ =
    µ0A
    		 =
    4π × 10–7 × π × (1.5 × 10–2)2
    L0.3

    = 29.6088 × 10–10
    L = 29.6088 × 10–10 × (103)2
    = 29.6088 × 10–4 H
    where,
    L = length of solenoid
    W = 1/2 LI2
    = 1/2 × 29.6088 × 10–4 × (10)2
    = 0.148 ≈ 0.15 J.

  1. If V, w, q stand for voltage, energy and charge, then V can be expressed as—








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    Since voltage is, broadly saying work per unit charge, we can express V as w/q, or V as dw/dq.

    Correct Option: B

    Since voltage is, broadly saying work per unit charge, we can express V as w/q, or V as dw/dq.

  1. Inside a hollow conducting sphere—








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

    Correct Option: A

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

  1. The expression for B, given that in free space E = 15 cos (6π × 108 t – 2πz) ix V/m is—








  1. View Hint View Answer Discuss in Forum

    The given wave is travelling in the + z direction (because of the presence of the term – 2 πz) and E is entirely in the x-direction. Now E and H direction gives the direction of travel of tower. It is concluded, therefore, that H must be in + y direction.
    ix × iy = iz
    Further, we know that

    | H | =
    |E|
    		and B = µ0 H
    η

    η = √
    µ0
    		or | B | =
    µ0 |E|
    ε0√µ0/ε0

    or
    B = E/V
    = ∵ = V
    1
    √µ0∈0

    or
    B =
    15 cos (6π × 108 t – 2πz) iy
    3 × 108

    or
    B = 5 × 10-8 cos (6π × 108 t – 2π z) iy Wb/m2

    Correct Option: A

    The given wave is travelling in the + z direction (because of the presence of the term – 2 πz) and E is entirely in the x-direction. Now E and H direction gives the direction of travel of tower. It is concluded, therefore, that H must be in + y direction.
    ix × iy = iz
    Further, we know that

    | H | =
    |E|
    		and B = µ0 H
    η

    η = √
    µ0
    		or | B | =
    µ0 |E|
    ε0√µ0/ε0

    or
    B = E/V
    = ∵ = V
    1
    √µ0∈0

    or
    B =
    15 cos (6π × 108 t – 2πz) iy
    3 × 108

    or
    B = 5 × 10-8 cos (6π × 108 t – 2π z) iy Wb/m2

  1. Following equations hold for time-varying fields—
    (i)
    ∇ × E = −
    ∂B
    ∂t

    (ii)
    E = − ∇ −
    ∂A
    ∂t

    (iii)
    ∇2V +
    ∂
    		(∇⋅A) =
    −ρv
    ∂tε

    (iv)
    →→
    B = ∇ × A

    (v)
    →→
    ∇ × H = J +
    ∂E
    ∂t








  1. View Hint View Answer Discuss in Forum

    Both V and →A are completely defined and thus can be evaluated.

    Correct Option: A

    Both V and →A are completely defined and thus can be evaluated.