Answer :

Given:


Resistance = R


Constant velocity = v


Formula used:


From previous question, induced emf


w, induced current = … (i), where E = emf, R = resistance, μ0 = magnetic permeability of vacuum, i = current in the wire, v = velocity of sliding rod, x = distance of centre of rod from wire, l = length of rod.


Now, magnetic force on element … (ii), where I = induced current, da = element, B = magnetic field due to infinitely straight wire


… (iii), where μ0 = magnetic permeability of vacuum, i = current in wire, a = distance from wire.


Hence, (ii) becomes


dF = integrating with suitable limits, we get



=>Force needed to keep the wire sliding at constant velocity v ns)


(b) Current I = E/R = here E = emf, R = resistance, μ0 = magnetic permeability of vacuum, i = current in the wire, v = velocity of sliding rod, x = distance of centre of rod from wire, l = length of rod. (Ans)


(c) Rate of heat developed in the resistor = Power(P) = I2R, where I = current, R = resistance


From previous part, I = therefore, rate of heat developed = (ans)


(d) Power delivered by external agent = rate of heat developed in resistor = (ans)


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