A closely wound coil has a radius of 5.70 cm and carries a current of 2.50 A . H

Question

A closely wound coil has a radius of 5.70 cm and carries a current of 2.50 A .

How many turns must it have if, at a point on the coil axis 5.30 cm from the center of the coil, the magnetic field is 6.31×104 T ?

I got about 70.048 N turns, but was incorrect.

Exercise 28.34 A closely wound coil has a radius of 5.70 cm and carries a current of 2.50 A. Part A How many turns must it have if, at a point on the coil axis 5.30 cm from the center of the coil, the magnetic field is 6.31x10 4T? 72 turns Submit My Answers Give Up Incorrect; Try Again; 3 attempts remaining Provide Feedback Continue

Explanation / Answer

B = (u0 n I / 2) ( r^2 / (x^2 + r^2)^(3/2))

putting values,

(x^2 + r^2)^(3/2) = (0.053^2 + 0.057^2)^(3/2) = 4.715 x 10^-4

6.31 x 10^-4 = (4pi x 10^-7 x n x 2.50 / 2) ( 0.057^2 / 4.715 x 10^-4)

6.31 x 10^-4 = (1.57 x 10^-6 n ) (6.89)

n = 58.3

hence 58 Or 59turns

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