A 121turn circular coil of radius 203 cm and negligible resi

A 121-turn circular coil of radius 2.03 cm and negligible resistance is immersed in a uniform magnetic field that is perpendicular to the plane of the coil. The coil is connected to a 19.1 omega resistor to create a closed circuit. During a time interval of 0.159 s the magnetic field strength decreases uniformly from 0.623 T to zero. Find the energy, in millijoules, that is dissipated in the resistor during this time interval.

Solution

The energy dissipated in the resistor is dependent on the current flowing through the resistor. The current in the circuit is dependent on the voltage produced as the magnetic field changes. The EMF, voltage, produced as the magnetic flux changes is dependent on the area of the coil and change of the magnetic field.

Magnetic flux = B * * r^2
B = 0.623 T
r = 2.03 cm = 0.0203 m
Magnetic flux = 0.623 * * 0.0203^2

EMF = (Number of turns) * ( Magnetic flux) ÷ (time interval)
EMF = 121 * (0.623 * * 0.0203^2) ÷ 0.159 = 0.613 volts

Current = EMF ÷ Resistance = 0.613 ÷ 19.1
Energy = I^2 * R * time = (0.613 ÷ 19.1)^2 * 19.1 * 0.159 = 0.00313 J = 3.13 mJ