First slide

Force on a current carrying wire placed in a magnetic field

Question

One end of a straight copper rod, carrying a current of 2A, is at the origin and the other end is at the point A whose co ordinates are (1m, 1m, 1m). A uniform magnetic field $\vec{B} = 1.5 \hat{i} T$ exists in that region, Direction of current in the rod is from the origin to point A. Then magnitude of force experienced by the rod is

Difficult

A

$3 N$
B

$2 \sqrt{2} N$
C

$3 \sqrt{2} N$
D

$4 \sqrt{3} N$

Solution

$\vec{F} = i \vec{l} \times \vec{B}$ . Here $\vec{l} = (\hat{i} + \hat{j} + \hat{k}) m$
$∴ \vec{F} = 2 (\hat{i} + \hat{j} + \hat{k}) \times 1.5 \hat{i} N = 3 (- \hat{k} + j) N$
$∴ F = 3 \sqrt{1^{2} + 1^{2}} N = 3 \sqrt{2} N$

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