Question

A small circular coil with a radius of 1.00 cm has 20 turns and carries a current. A magnetic field probe is located somewhere along the coil's central axis, much farther from the coil's center than the coil's radius.

A. The probe indicates that the magnetic field points down the axis, towards the center of the coil. Looking down the axis towards the coil, the current must be flowing which way? (clockwise or counterclockwise)

B. At a distance of 3.0 meters from the center of the coil, the probe indicates that the coil's magnetic field has a magnitude of 13.0 pT (10^-12 T). How much current is flowing in the coil?

C.How strong is the field at the center of the coil, in Gauss?

D. If the probe is moved to a distance of 9.0 meters from the center of the probe, how much weaker the magnetic field it detects be?

Answer 1

a)

Using right hand curl rule , the direction of current in the circular coil must be clockwise

Clockwise

b)

a = radius of the circular coil = 1 cm = 0.01 m

n = number of turns of coil = 20

x = distance of the probe from the center of coil = 3 m

i = current in the coil = ?

B = magnetic field at the location of the probe = 13 x 10^-12 T

Magnetic field by a circular coil along at some distance from the center along its axis is given as

B = (/4) (2 n a² i /(a² + x²)^3/2)

inserting the values

13 x 10^-12 = (10^-7) (2(3.14) (20) (0.01)² i /((0.01)² + (3)² )^3/2)

i = 0.28 A

c)

At the center of the coil, magnetic field is given as

B = (/4) (2 n i/a)

B = (10^-7) (2(3.14) (20) (0.28)/0.01)

B = 3.5 x 10^-4 T

B = 3.5 Gauss

d)

at x = 9

Magnetic field by a circular coil along at some distance from the center along its axis is given as

B = (/4) (2 n a² i /(a² + x²)^3/2)

inserting the values

B = (10^-7) (2(3.14) (20) (0.01)² (0.28) /((0.01)² + (9)² )^3/2)

B = 4.82 x 10^-13 T