A circular circuit of diameter D = 60 cm and 20 loops is inside a uniform magnet

Question

A circular circuit of diameter D = 60 cm and 20 loops is inside a uniform magnetic field directed originally into the plane of the circuit. The magnetic field is changed steadily from 3.2 T into the page to 1.4 T out of the page in 4 seconds. Calculate the induced current and its direction? For part (a), what is direction of the induced magnetic field? An average electric power of 120 W is transmitted from a power plant to a town over transmission lines. The transmission liens have a resistance of 0.4 Ohm. Calculate the power losses if the power is transmitted with i) 240 V ii) 2400 V.

Explanation / Answer

(A) Bi = - 3.2 T

Bf = 1.4 T

induced emf = rate of change of magnetcic flux = d(NBA)dt

= N A dB/dt

= (20) (pi 0.60^2 / 4) (1.4 + 3.2) / 4

= 6.50 Volt

resistance is not given. That is needed to find current.

Induced current = 6.50 volt / R

put R in ohm and get current in Amperes.

direction -> clockwise

(B) into the page

(C) Power losses = V^2 / R

(i) 240^2 / 0.4 = 144000 W

(ii) 2400^2 / 0.4 = 14.4 x 10^6 W

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