The magnetic field existing in a region is given by . A square loop of edge 50 cm carrying 0.5 A current is placed in the x – y plane with its edges parallel to the x – y axes, as shown in the figure. The magnitude of the net magnetic force experienced by

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Solution

Q.
The magnetic field existing in a region is given by $\vec{B} = 0.2 (1 + 2 x) \hat{k} T$ . A square loop of edge 50 cm carrying 0.5 A current is placed in the x – y plane with its edges parallel to the x – y axes, as shown in the figure. The magnitude of the net magnetic force experienced by the loop is ______ mN. [2024]

Ans.
(50)

$\vec{F} = i (\vec{ℓ} \times \vec{B})$

$F_{3} and F_{4} will cancel each other.$

${\vec{F}}_{1} = - 0.5 \times \frac{50}{100} \times {0.2 (1 + 4)} \hat{i}$

$= - \frac{1}{2} \times \frac{1}{2} \times 1 \hat{i} = - \frac{1}{4} \hat{i} = - 0.25 \hat{i}$

${\vec{F}}_{2} = 0.5 \times \frac{50}{100} \times {0.2 (1 + 5)} \hat{i} = \frac{1}{2} \times \frac{1}{2} \times {1.2} \hat{i} = 0.3 \hat{i}$

${\vec{F}}_{net} = 0.05 \hat{i} (N) = 50 (mN) \hat{i}$

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