A piece of copper wire is formed into a single circular loop of radius 13 cm. A magnetic field is oriented parallel to the normal to the loop, and it increases from 0 to 0.86 T in a time of 0.67 s. The wire has a resistance per unit length of 4.4 x 10-2 /m. What is the average electrical energy dissipated in the resistance of the wire? Number Units

0.07 J

Explanation:

Parameters given:

Radius of loop, r = 13 cm = 0.13 m

Change in magnetic field, B = 0.86 T

Time taken, t = 0.67 s

Resistance per unit length of wire, R/L =

Resistance in the entire length of wire, R = R/L * L (where L = circumference of wire)

R =

R = 0.036 ohms

Electrical energy is given as the product of Power and Time;

E = P * t

Electrical power, P, is given as:

where V = EMF/Voltage

The average EMF induced in a coil is given as:

where A = Area of coil = =

Therefore, Power becomes:

Then, Electrical energy becomes:

The average electrical energy dissipated in the resistance of the wire is 0.07 J