A 1 m long metal rod XY completes the circuit as shown in the figure. The plane of the circuit is perpendicular to the magnetic field of flux density 0.15 T. [2023]

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Solution

Q.
A 1 m long metal rod XY completes the circuit as shown in the figure. The plane of the circuit is perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the circuit is $5 Ω$ , the force needed to move the rod in the direction, as indicated, with a constant speed of 4 m/s will be ________ $10^{- 3} N$ . [2023]

Ans.
(18)

$F = i l B$

$= (\frac{ε}{R}) l B = (\frac{v B l}{R}) l B = \frac{v B^{2} l^{2}}{R} = \frac{4}{5} \times {(\frac{15}{100})}^{2} \times 1^{2}$

$= \frac{4}{5} \times \frac{225}{10^{4}} = \frac{180}{10^{4}} = 0.018 N = 18 \times 10^{- 3} N$

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