• # question_answer A rectangular loop shaped wire KLMN is moved with a uniform velocity v at right angle to a uniform magnetic field B as shown in the figure. (i) What is the magnitude of current induced in the loop? (ii) Will there be any work done by the loop? Give reason for your answer. (iii) If the magnetic flux linked with the loop is given by ${{\phi }_{m}}=6{{t}^{3}}-4{{t}^{2}}+2t+20,$ then calculate the induced emf in the coil at t = 4s

(i) Magnitude of current induced in the loop is zero, as there is no change in magnetic flux through the loop. (ii) No, work is not done by the loop as there is no change in magnetic flux through the loop. According to Lenz's law, there is no force to oppose the motion, so work done is zero. (iii) Given,          ${{\phi }_{m}}=6{{t}^{3}}-4{{t}^{2}}+2t+20$ Since, we know that, Induced emf, $e={{\left| \frac{d{{\phi }_{m}}}{dt} \right|}_{at\,t={{t}_{1}}}}$ $\therefore$      $\frac{d\phi }{dt}=18{{t}^{2}}-8t+2$ Putting the value of t = 4 in above equation,             $e=[18\times {{4}^{2}}-8\times 4+2]=258\,V$

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