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In the figure shown a conducting rod of length l, resistnace R and mass m is moved with a constant velocity v.The magnetic field B varies with time t as B=5 t, where t is time in second.At t=0 the area of the loop containing capacitor and the rod is zero and the capacitor is uncharged.The rod started moving at t=0 on the fixed smooth conducting rails which have negligible resistance.Find (i)The current in the circuit as a function of time t. (ii)If the above system is kept in vertical plane such that the rod can move vertically downward due of gravity and other parts are kept fixed and B=constant =B_(0).then find the maximum current in the circuit. |
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Answer» =`BA=(5t)(lvt)=5lvt^(2)` `therefore epsilon =|(dphi)/(dt)|=10 l vt` `q/C=epsilon-IR rArr q/c=10l vt -iR` Differentiating both SIDES w.r.t `t` `10lv-(di)/(dt)R=i/c` `i=10 LVC(1-e^(-t//cR))` (ii)`q//c=epsilon-iR=BVl-IR`, for maximum value of `i,di//dt=0` `i//c=Bal-di//dtxxR` `l//c=B((mg-Bil)/m)l-0` `therefore i=i_(max)=(mg Bl c)/(m+B^(2)l^(2)c)` 
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