A student has of insulated copper wire and wishes to construct an electromagnet that…

PHYSICS · Multi-part · CBSE · Physics · Magnetic Effects of Electric Current · Magnetic Effects of Electric Current

Problem

A student has

10\,\text{m}

of insulated copper wire and wishes to construct an electromagnet that produces a magnetic field of

2.0\,\text{mT}

at its center. The design calls for winding the entire length of wire into

N

tightly packed circular turns of identical radius

r

, all lying in the same plane and sharing a common center. Assume any spacing between adjacent turns is negligible compared with

r

. The laboratory power supply can provide a maximum continuous current of

5.0\,\text{A}

. Neglect any interaction between turns other than field superposition. Complete the tasks below, symbolically where requested and numerically where possible. (a) Derive an expression for the magnetic field magnitude at the center of the multi-turn coil in terms of the total wire length

L

, the chosen radius

r

, and the current

I

. (b) Using

L=10\,\text{m}

and

I=5.0\,\text{A}

, determine the coil radius required to achieve the target field of

2.0\,\text{mT}

. Give your answer to an appropriate number of significant figures. (c) Suppose the student instead chose a radius

20\%

smaller than the value found in part (b) while keeping the current at

5.0\,\text{A}

. Without additional calculation, state whether the resulting field at the center would be greater than, equal to, or less than

2.0\,\text{mT}

and briefly justify your answer based on the dependence revealed in part (a).

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