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A 1 cm segment of a wire lying along x -axis carries current of 0.5 A along +x direction. A magnetic field \(\vec{B}=(0.…

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A 1 cm segment of a wire lying along x -axis carries current of 0.5 A along +x direction. A magnetic field \(\vec{B}=(0.4\mathrm{mT})\overset{^}{j}+(0.6\mathrm{mT})\overset{^}{k}\) is switched on, in the region. The force acting on the segment is

a

\((2\overset{^}{j}+3\overset{^}{k})\mathrm{mN}\)

b

\((-3\overset{^}{j}+2\overset{^}{k})\mu \mathrm{N}\)

c

\((6\overset{^}{j}+4\overset{^}{k})\mathrm{mN}\)

d

\((-4\overset{^}{\mathrm{j}}+6\overset{^}{\mathrm{k}})\mu \mathrm{N}\)

✓ Correct answer: b)

\((-3\overset{^}{j}+2\overset{^}{k})\mu \mathrm{N}\)

Explanation\[\mathbf{L} \times \mathbf{B} = (0.01 \, \text{m})\mathbf{\hat{i}} \times [(0.4 \times 10^{-3} \, \text{T})\mathbf{\hat{j}} + (0.6 \times 10^{-3} \, \text{T})\mathbf{\hat{k}}]\]

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