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?
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 cm2
= 16 × 10−4 m2
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 = i2R
= (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.
