3.66 A Constants Previous Answers A closely wound, circular coil with radius 2.3

Question

3.66 A Constants Previous Answers A closely wound, circular coil with radius 2.30 cm has 770 turns Correct Significant Figures Feedback: Your answer 3.7 A was either rounded differently or used a different number of significant figures than required for this ar Part B At what distance from the center of the coil, on the axis of the coil, is the magnetic field half its value at the center? Express your answer to three significant figures and include the appropriate units. HA VUnits alue Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining

Explanation / Answer

Magnetic field at the center of coil is given by

Bc = u0*N*i/(2*r)

Magnetic field at the axis of coil is given by:

Ba = u0*N*i*r^2/(2*(x^2 + r^2)^(3/2))

Now given that

Ba = Bc/2

u0*N*i*r^2/(2*(x^2 + r^2)^(3/2)) = u0*N*i/(2*2*r)

r^2/(2*(x^2 + r^2)^(3/2)) = 1/(2*r)

2*r^3 = (x^2 + r^2)^(3/2)

x = sqrt [2^(2/3)*r^2 - r^2]

Using given value

x = sqrt [2^(2/3)*0.023^2 - 0.023^2]

x = 0.0176 m

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