Question

If an electric wire is allowed to produce a magnetic field no larger than that of the Earth (0.55 x 10-4 T) at a distance of 25 cm, what is the maximum current the wire can carry?

Answer 1

68.75 A

Step-by-step explanation:

B = 0.55 x 10^-4 T, r = 25 cm = 0.25 m

Let the current be i.

The magnetic field due to a current carrying straight wire at a distance r is given by

B = μ0 / 4π x 2 i / r

0.55 x 10^-4 = 10^-7 x 2 x i / 0.25

i = 68.75 A

Answer 2

we are given in the problem the following dimensions or specifications
B = 0.000055 T r = 0.25 m constant mu0 = 4*pi*10-7

The formula that is applicable from physics is
B = mu0*I/(2*pi*r) I = 2*B*pi*r/mu0 I = 68.75 Amperes