Question

A cylindrical conductor of radius R = 9 cm has a non-uniform current density J = 2 r^2 in units of A/m2 P (a) Calculate the magnetic field at distance r = 8 cm from the center of the conductor. Select one: O a. 107.67 O b. 121.00 O c. 362.00

Answer 1

One can use the Ampere law to calculate the magnetic field (B) (magnitude). Imagine a cyclinder with radius and some height as the Ampere surface. Now the current enclosed is,
Tenc pi Jda 521 2r2r' dr' dᎾ 4 А.

Now Ampere Law says (basically the cousin of Gauss' Law for magnetostatics),
Bdl = Holenc
As before imagine a cylinder of radius and of finite length symmetrically covering the current charge distribution. So at a radius (inside the cylinder) we have,
3 B(2nr) = Holenc = Monr4 B=

Plugging in the values,
r = 8.0 x 10-2 m
we get,
B = 3.21699 x 10-10 T.

Note: The options that you have provided lacks units. I've provided the answer in SI units.