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The magnitude of the magnetic induction vector B due to a thin, infinite plane carrying a current of linear density $i$ is $B = μ_{0} i / 2$ . (Assume the vector $i$ is the same at all points of the plane)

The magnitude of the magnetic induction vector B due to two, thin parallel infinite planes carrying currents of linear densities $i$ and $- i$ is $B = μ_{0} i$ between the planes and B = 0 outside the planes

The magnitude of the magnetic induction vector B due to two thin, parallel infinite planes carrying currents of linear densities $i$ and $i$ is $B = μ_{0} i$ between the planes and B = 0 outside the planes

The magnitude of the magnetic induction vector B due to two thin, parallel infinite planes carrying currents of linear densities $- i$ and $- i$ is $B = μ_{0} i$ between the planes and B = 0 outside the planes

answer is A, B.

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Detailed Solution

Apply Ampere's circuital law,

(A) Consider Amperian loop as in derivation of B due to a solenoid. Option (A) is correct.
(B) Two magnetic fields $B = \frac{μ_{0} i}{2}$ point in the same direction in-between the plates. They point in opposite direction in region outside the plates. Option (B) is correct.
(C) Two magnetic fields $B = \frac{μ_{0} i}{2}$ point in the opposite directions in-between the plates. They point in same direction outside the plates. Option (C) is wrong.
(D) Two magnetic fields $B = \frac{μ_{0} i}{2}$ point in the opposite directions in-between the plates. They point in same direction outside the plates. Option (D) is wrong.