2. Part A Two concentric current loops lie in the same plane. The smaller loop h

Question

2.

Part A

Two concentric current loops lie in the same plane. The smaller loop has a radius of 3.5 cm and a current of 12 A. The bigger loop has a current of 20 A . The magnetic field at the center of the loops is found to be zero.

What is the radius of the bigger loop?

Express your answer to two significant figures and include the appropriate units.

Part B

A researcher would like to perform an experiment in a zero magnetic field, which means that the field of the earth must be canceled. Suppose the experiment is done inside a solenoid of diameter 1.0 m, length 3.0 m , with a total of 5000 turns of wire. The solenoid is oriented to produce a field that opposes and exactly cancels the 52 T local value of the earth's field.

What current is needed in the solenoid's wires?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

PART A

The B-field at the center of a circular loop of radius "r" and current "i" is;

B = ui/2r

The field is along the axis , one way for counterclockwise current and the other direction for clockwise current.

So, assume the current in the large loop is in the opposite direction and the set its field equal to the field of the small loop;

uI/2R = ui/2r

R = rI/i

= (3.5)(20)/(12)

= 5.83 cm

PART B

r:  Using Ampere's Law, the magnetic field produced inside this solenoid is given by

B = uo N I / h

where uo is the vacuum permeability, N is the number of turns in the solenoid and h is the length of the solenoid. Earth's magnetic field is around 50 microteslas in North America thus the current needed in the solenoid is

I = B h / (uo N) = (52 E-6 ) (4) / ((4 pi E-7)(5200) ) = 0.031 A

I = 31 mA

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