Consider a

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)