Question

1.)

Part A

An investigator places a sample 1.0 cm from a wire carrying a large current; the strength of the magnetic field has a particular value at this point. Later, she must move the sample to a 11.0 cmdistance, but she would like to keep the field the same.

By what factor must she increase the current?

Part B

The small currents in axons corresponding to nerve impulses produce measurable magnetic fields. A typical axon carries a peak current of 0.040 μA.

What is the strength of the field at a distance of 2.0 mm ?

Express your answer with the appropriate units.

Part C

A solenoid used to produce magnetic fields for research purposes is 1.6 m long, with an inner radius of 30 cm and 1500 turns of wire. When running, the solenoid produced a field of 1.5 T in the center.

Given this, how large a current does it carry?

Answer 1

Part A

By a factro of 3

Part B

Treat the axon as a long current-carrying wire. The field at a distance r (in metres) is given by:
B = μ0.I/(2.π.r)

B = (4π x 10^-7) x (0.040 x 10^-6) / (2 x π x 2.0 x 10^-3)

= 4.0 x 10^-12 T

Part C

The magnetic field inside a solenoid is given by: B = µo NI

where,

permeability of free space: µ0 = 4πx10^-7 T/m-A

turns per unit length: N = 1500/1.6 = 937.5

magnitude of magnetic field: B = 1.5 T

solenoid current: I = B/µoN = 1.5 / (937.5*4πx10^-7)

I = 1273 A