Question

A 2.8 mm -diameter copper wire carries a 31 Acurrent (uniform across its cross section).

A) Determine the magnetic field at the surface of the wire.

B) Determine the magnetic field inside the wire, 0.50 mm below the surface.

C) Determine the magnetic field outside the wire 2.5 mm from the surface.

Answer 1

given d = 2.8 mm = 2.8 X 10^-3 m

r = 1.4 X 10^-3 m

i = 31 A

a )

B = _o i / 2 r

= 4 X 3.14 X 10^-7 X 31 / 2 X 3.14 X 1.4 X10^-3

B = 4.42 X10^-3 T

B = 4.42 mT

b )

using = i / A

= i / r²

= 33 / ( 3.14 X 1.4² X 10^-6 )

= 5.362 X 10⁶ A m²

I ' = A

= X 3.14 X r²

I ' = 5.362 X 10⁶ X 3.14 X ( 1.4 - 0.5 )² X 10^-6

I ' = 32.99

I ' = 13.63 A

B = _o I ' / 2 r

B = 2 X 10^-7 X 13.63 / ( 1.4 - 0.5 ) X 10^-3

B = 3.0288 X 10^-3 T

B = 3.0288 m T

c )

r = 1.4 + 2.5 = 3.9 mm = 3.9 X 10^-3 m

B = _o i / 2 r

B = 2 X 10^-7 X 31 / ( 3.9 ) X 10^-3

B = 1.589 X 10^-3 T

B = 1.589 mT