Question

A circular loop of wire with radius 0.0410 m and resistance 0.169 Ω is in a region of spatially uniform magnetic field, as shown in the following figure (Figure 1). The magnetic field is directed out of the plane of the figure. The magnetic field has an initial value of 7.78 T and is decreasing at a rate of -0.605 T/s.
a) Is the induced current in the loop clockwise or counterclockwise?
b) What is the rate at which electrical energy is being dissipated by the resistance of the loop?

Answer 1

(a) The induced current in the loop will be counterclockwise.

(b) The rate at which electrical energy is being dissipated by the resistance of the loop is 0.012 W.

Direction of the current

The induced current in the loop will be counterclockwise to the direction of magnetic field.

Emf induced in the loop

emf = -NdФ/dt

emf = -NBA/dt

where;

A is area of the loop

A = πr² = π(0.041)² = 5.28 x 10⁻³ m²

emf = -(-0.605 - 7.78) x 5.28 x 10⁻³

emf = 8.385 x 5.28 x 10⁻³

emf = 0.0442 V

Rate of energy dissipation

P = emf²/R

P = (0.0442)²/0.169

P = 0.012 W

Thus, the rate at which electrical energy is being dissipated by the resistance of the loop is 0.012 W.

Learn more about power dissipation here: brainly.com/question/15015986

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