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Question

A long straight wire carries a current of $$50\, A$$. An electron moving at $$10^7\, m/s$$ is $$5\, cm$$ away from the wire. The force acting on electron if its velocity is directed towards the wire will be :


A
1.6×106N
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B
3.2×1016N
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C
4.8×1016N
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D
1.8×1016N
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Solution

The correct option is C $$3.2\times 10^{-16}\, N$$
Given: Current in wire= 50A
            Speed of electron=$$10^{7}ms^{-1}$$
Solution: Let us assume the current is directed in +y direction.
As we know, magnetic field due to straight wire is given by,
$$B=\frac{\mu _{0}i}{2\pi r}$$
$$=\frac{4\pi \times 10^{-7}\times 50}{2\pi \times 0.05}$$
$$=0.0002T$$
According to question, v and B are perpendicular to each other.
$$F=qvb$$
Substituting the values we get,
$$=1.6\times 10^{-19}\times 10^{7}\times 0.0002$$
$$=3.2\times 10^{-16}N$$
Hence, the correct option is (B).

Physics

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