A uniform magnetic field is normal to the plane of a circular loop 14 cm in diam

Question

A uniform magnetic field is normal to the plane of a circular loop 14 cm in diameter and made of copper wire (of diameter 5.0 mm). (a) Calculate the resistance of the wire. (b) At what rate must the magnetic field change with time if an induced current of 10 A is to appear in the loop?l An alloy specifically designed to have a small value of a. pure silicon doped with phosphorus impurities to a charge carrier density of 10^23 m^-3. Pure silicon doped with aluminum impurities to a charge carrier density of 10^23 m^-3.

Explanation / Answer

a.

R = L / A

L = * 14 * 10^-2 = 0.44

A = * (2.5*10^-3)^2 = 1.96*10^-5

=> R = (1.69*10^-8)*(0.44)/(1.96*10^-5) = 3.79*10^-4

b.

= -db/dt

I/R = -db/dt

where

I = 10A

R = 3.79*10^-4

-db/dt   is the rate of change change for flux

so

10/(3.79*10^-4) = 2.64*10^4 T

and it may have a negative sign depends on the direction of the current.

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