A piece of copper wire is formed into a single circular loopof radius 11 cm. A m

Question

A piece of copper wire is formed into a single circular loopof radius 11 cm. A magnetic field isoriented parallel to the normal to the loop, and it increases from0 to 0.65 T in a time of 0.45 s. The wirehas a resistance per unit length of 3.3 X10-2 ohms/m. What is the average electricalenergy dissipated in the resistance of the wire.
1 J
A piece of copper wire is formed into a single circular loopof radius 11 cm. A magnetic field isoriented parallel to the normal to the loop, and it increases from0 to 0.65 T in a time of 0.45 s. The wirehas a resistance per unit length of 3.3 X10-2 ohms/m. What is the average electricalenergy dissipated in the resistance of the wire.
1 J

Explanation / Answer

Given that the radius of loop is r = 14 cm = 0.11 m The change in magnetic field is dB = 0.65T - 0 T = 0.65 T Time taken is t = 0.45 s Resistance per unit length is R / L =3.3*10-2 /m     The angle between the magnetic field and normal of plane is = 0o ----------------------------------------------------------------------- The induced emf is V = d / dt                                 = d ( B.A) /dt                                  = d( BA cos) /dt                                 = A*dB/dt                                 = ( r )2 dB/dt                                       = 0.054 V The length of conductor is L = 2r = 0.69 m Then the resistance is R = (R/L)*L =2.27*10-2 Energy dissipated is U = V 2 / R                                    = 0.1279 J

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