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  4. A rectangular loop with a sliding connector of length l=1.0 m is situated in a uniform magnetic field B=2 T perpendicular to the plane of loop. Resistance of connector is r=2 Ω. <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/075e171d4ae01165e75d28967a6739ef-.png /> Two resistances of 6 Ω and 3 Ω are connected as shown in the figure. Find the external force (in newton) required to keep the connector moving with a constant velocity v=2 m / s.

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Q. A rectangular loop with a sliding connector of length $l=1.0\, m$ is situated in a uniform magnetic field $B=2 T$ perpendicular to the plane of loop. Resistance of connector is $r=2\, \Omega$.
image
Two resistances of $6\, \Omega$ and $3\, \Omega$ are connected as shown in the figure. Find the external force (in newton) required to keep the connector moving with a constant velocity $v=2\, m / s$.

Electromagnetic Induction

Solution:

image
$R_{\text{eff }}=\frac{3 \times 6}{3+6}+2=4\, \Omega$
$\therefore I=\frac{\varepsilon}{R_{ cff }}=\frac{B l v}{R_{\text{eff }}}=\frac{2 \times 1 \times 2}{4}=1\, A$
$\therefore F=I l B=1 \times 1 \times 2=2\, N$