First slide

Force on a current carrying wire placed in a magnetic field

Question

A rectangular coil ABCD carrying a current of 2A is placed in a uniform magnetic field of induction magnetic field of induction B = 2 T in a gravity free space. Length Ab = CD = 4 m and length BC = Ad = 3 m. Then tensions induced in the sides AB and BC are respectively.

Moderate

A

8 N, 16 N
B

12 N, 16 N
C

8 N, 4 N
D

6 N, 8 N

Solution

$\begin{array}{rcl} T_{AB} & = & T_{CD} = \frac{1}{2} i (BC) . B \\ = & \frac{1}{2} \times 2 \times 3 \times 2 N = 6 N \\ T_{BC} & = & \frac{1}{2} . i (AB) . B = \frac{1}{2} \times 2 \times 4 \times 2 N = 8 N \end{array}$

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