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Suppose the loop is stationary but the current feeding the electromagnet that produces the magnetic field is gradually reduced so that the field decreases from its initial value of 0.3 T at the rate of 0.02 T s^{−1}. If the cut is joined and the loop has a resistance of 1.6 Ω how much power is dissipated by the loop as heat? What is the source of this power?

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#### Solution

Sides of the rectangular loop are 8 cm and 2 cm.

Hence, area of the rectangular wire loop,

A = length × width

= 8 × 2

= 16 cm^{2}

= 16 × 10^{−4} m^{2}

Initial value of the magnetic field, B' = 0.3 T

Rate of decrease of the magnetic field, `("dB")/("dt")` = 0.02 T/s

Emf developed in the loop is given as:

`"e" = ("d"phi)/("dt")`

Where,

`"d"phi` = Change in flux through the loop area = AB

∴ e = `("d"("AB"))/("dt") = ("AdB")/"dt"`

= 16 × 10^{−4} × 0.02

= 0.32 × 10^{−4} V

Resistance of the loop, R = 1.6 Ω

The current induced in the loop is given as:

i = `"e"/"R"`

= `(0.32 xx 10^-4)/(1.6)`

= 2 × 10^{−5} A

Power dissipated in the loop in the form of heat is given as:

P = i^{2}R

= (2 × 10^{−5}) × 1.6

= 6.4 × 10^{−10} W

The source of this heat loss is an external agent, which is responsible for changing the magnetic field with time.

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