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A wire ab of length $\sqrt{3}$ metre, mass m = 1 kg and resistance $R = 0.45 Ω$ slide on a smooth, thick pair of metallic rails joined at the bottom as shown in figure. The plane of the rails makes an angle $θ$ with the horizontal. A vertical magnetic field B exists in the region. If the wire slides on rails at a constant speed of 1 m/s. Then $[{g=10m/s}^{2}]$

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Force acting on wire is 5 N

Magnetic force is 3 N

Magnetic field is 1 T

Magnetic force acting on wire is $\frac{10}{\sqrt{3}} N$

answer is A, D.

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Detailed Solution

$E=BVlcosθ .... (i)$

$I= \frac{BVlcosθ}{R} .... (ii)$

$F=IIB$

$F= \frac{BVlcosθ}{R} IB$

$F= \frac{B^{2} {Vl}^{2}}{R} cosθ ... (iii)$

$ma=mgsinθ-Fcosθ=0$

$mgsinθ= \frac{B^{2} {Vl}^{2} cosθ}{R} cosθ$

$B= \sqrt{\frac{mgRsinθ}{{Vl}^{2} {cos}^{2} θ}}$

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