Question

A circular loop of 22 turns and 46.3 cm diameter is directed perpendicular to a magnetic field of 356 mT. The wire itself has a diameter of 4.2 mm and is made of copper. If the magnetic field is uniformly decreased from 356 mT to zero, how much charge moves past a single point on the coil during this time?

Answer 1

N = number of turns of the loop = 22

D = diameter of the loop = 46.3 cm = 0.463 m

R = radius of the loop = D/2 = 0.463/2 = 0.2315 m

length of the wire is given as

L = N (2R)

L = (22) (2 (3.14) (0.2315))

L = 31.984 m

A = Area of the loop = R2 = (3.14) (0.2315)2 = 0.1683 m2

B = Change in magnetic field through the loop = 0 - 356 mT = - 356 mT = - 0.356 T

d = diameter of wire = 4.2 mm = 0.0042 m

r = radius of the wire = d/2 = 0.0042/2 = 0.0021 m

Area of cross-section of the wire is given as

a = r2 = (3.14) (0.0021)2 = 1.4 x 10-5 m2

= resistivity of copper = 1.68 x 10-8

resistance of the wire is given as

R = L/a = ( 1.68 x 10-8) (31.984) /(1.4 x 10-5)

R = 0.03838 ohm

induced current in the wire is given as

i = - N A B/t

i t = - N A B

q = - N A B (Since q = i t )

q = - (22) (0.1683) (- 0.356)

q = 1.32 C