Calculating Jupiter's Magnetic Dipole Moment Using a Dipole Approximation

[Noreturn]

Homework Statement

Jupiter has the strongest magnetic field in our solar system, about 14 G at its poles.
Approximating the field as that of a dipole, find Jupiter's magnetic dipole moment

radius= 69.9*x10^6

Homework Equations

u=2UB
or
T=U*B

The Attempt at a Solution

T= (14x10^-4)*(.138*10^3)
.1932 A*M^2

Which is wrong
So then I tried:
2(14.4x10^-4)(.138*10^3)
.3864 A*M^2

Edit just noticed that I had units wrong on the diameter of Jupiter. If I change the calculation to:

T=(14*10^-4)(1.38*10^8)
we get: 1.932*10^5 A*M^2

Is that right?

 

[TSny]

Can you define the meaning of the symbols in the equation T = U*B?

 

[kuruman]

I don't see the equation giving the field of a dipole as a function of position among the numbers that you posted. Look for it here.
https://en.wikipedia.org/wiki/Magnetic_dipole

 

[Noreturn]

That one sounds more correct. M is a magnetic moment constant (14G in our case) and radius is 69.9*10^6m.

So then that works out to be:
2.6*10^29 A/M^2

Those equations were wrong because it was equation for torque. And B was magnetic strength.

 

[kuruman]

Your expression $\frac{\vec{m}\cdot \vec{r}}{4\pi r^3}$ is off by a factor of 2μ₀.

 

[Noreturn]

So equation is:

2Uo(M*r/4pir^3)

So 6.5*10^23

 

[kuruman]

No, the equation is given in the Wikipedia link that I posted in #3. Use that with $\vec{r}$ being the position vector of Jupiter's pole.