HardPhysics
+4 / -1
A straight copper wire of length 1 m is placed perpendicular to the plane of magnetic field B = (i + 3k) T. If the wire moves with velocity v = (3i + 2j + k) m/s, then magnitude of motional emf across its ends will be
A
4 V
B
8 V
C
6 V
D
12 V
Explanation
Motional emf ε = |(v × B) · L|. First, calculate v × B = |i j k; 3 2 1; 1 0 3| = i(6-0) - j(9-1) + k(0-2) = 6i - 8j - 2k. The wire length vector L is perpendicular to the B-field plane. For a 1m wire, the magnitude is simply the component of (v × B) along the wire. Given the constraints and typical orientation, ε = 6 V.
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