A long straight wire of length 2 m and mass 250 g is suspended horizontally in a uniform horizontal magnetic field of 0.7 T. The amount of current flowing through the wire will be ( ) [2023]

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Solution

Q.
A long straight wire of length 2 m and mass 250 g is suspended horizontally in a uniform horizontal magnetic field of 0.7 T. The amount of current flowing through the wire will be ( $g = 9.8$ $m$ $s^{- 2}$ ) [2023]

1 2.45 A

2 2.25 A

3 2.75 A

4 1.75 A

Ans.
(4)

Weight of the wire, $F = m g$ ...(i)

Force acting on the current carrying wire, $F = I (\vec{l} \times \vec{B})$ ...(ii)

Equating eq(i) and (ii)

$m g = I l B \sin 90 °$

$m g = I l B$

$I = \frac{m g}{l B} = \frac{250 \times 10^{- 3} \times 9.8}{2 \times 0.7}$

$I = 1.75$ $A$

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