Answer:
A) Dipole moment; m = 8.02 x 10^(22) J/T
B) I = 3.51 x 10^(9) A
Explanation:
The components of a magnetic field of a dipole are;
B_r = (μ_o•m/2πr³).cosθ
B_θ = (μ_o•m/4πr³).sin θ
B_Φ = 0
Let's make m the subject in the B_r equation ;
m = (2πr³•B_r)/(μ_o•cosθ)
Where;
B_r is magnetic field = 0.62 Gauss = 6.2 x 10^(-5) T
μ_o is the magnetic constant and has a value of 4π × 10^(−7) H/m
m is magnetic moment.
r is equal to radius of earth =6.371 x 10^(6)m
Thus, if we set θ = 0,we can solve for m as below;
m = (2π(6.371 x 10^(6))³•6.2 x 10^(-5) )/(4π × 10^(−7)•cos0)
Thus, m = 8.02 x 10^(22) J/T
B) Now, to find the current, let's use the expression for the magnetic field on the z-axis of the current ring.
B_z = (μ_o•Ib²/(2(z² + b²/2)^(3/2)))
So, let's set z = R and b = R/2
Thus, we now have;
B_z = (μ_o•I)/(5^(3/2)•R)
Making I the subject, we have;
I = [(5^(3/2)•R)•B_z]/μ_o
Plugging in the relevant values, we have;
I = [(5^(3/2) x 6.371 x 10^(6)) x 6.2 x 10^(-5)]/(4π × 10^(−7))
I = 3.51 x 10^(9) A
