(14%) Problem 5: Since moving charges create magnetic fields and magnetic fields

Question

(14%) Problem 5: Since moving charges create magnetic fields and magnetic fields exert forces on moving charges, devices that are used to measure field strengths often affect the system they are being used to measure. Consider the wire segment in the figurc, which is uscd to mcasure the magnetic ficld by determining the force exerted on the current flowing through it Bout 20.0 cm Otheexpertta.com M e 50% Part (a) Estimate the field the loop creates by calculating the field strength diameter carrying 6.5 A. in teslas, at the center of a circular loop 20.0 cm in 50% Part (b) what is the smallest field strength this loop can be used to measure with a 65-A current, if its field should alter the measured field by 0.0100% or less?

Explanation / Answer

Given,

d = 20 cm => r = 10 cm ; I = 6.5 A

a)We know that,

B = u0 I/2 r

B = 4 pi x 10^-7 x 6.5/2 0.1 = 4.08 x 10-5 T

Hence, B = 4.08 x 10^-5 T

b)4.08 x 10^-5 T /(0.01/100) = 0.408 T

Hence, B = 0.408 T

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