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  4. A 0.5 m long metal rod PQ completes the circuit as shown in the figure. The area of the circuit is perpendicular to the magnetic field of flux density 0.15 T . If the resistance of the total circuit is 3 Ω , calculate the force needed to move the rod in the direction as indicated with a constant speed of 2 textm s−1. <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-q8m2ryly7tnc.png />

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Q. A $0.5 \, m$ long metal rod $PQ$ completes the circuit as shown in the figure. The area of the circuit is perpendicular to the magnetic field of flux density $0.15 \, T$ . If the resistance of the total circuit is $3 \, \Omega ,$ calculate the force needed to move the rod in the direction as indicated with a constant speed of $2 \, \text{m s}^{−1.}$

Question

NTA AbhyasNTA Abhyas 2020

Solution:

$F = \frac{B^{2} \, l^{2} \, v}{R} = \frac{\left(\right. 0.15 \left.\right)^{2} \left(\right. 0.5 \left.\right)^{2} \times 2}{3}$
$= 0.00375 \, N$
$= 3.75 \, \text{mN}$