Magnetostatics. Degree Level.

A cylindrical column of mercury of radius a carries a current I, uniformly distributed over its cross-section. By considering the force per unit volume on the current, derive a formula for the pressure p as a function of radius r in the column (ignoring the weight of the mercury). If a = 5 mm and I = 100 A, what is the difference between the pressure at the centre and that on the edge of the column?

Thanks.

Reply 1

TableChair

1

Right how far have you got?

First draw a diagram of it. Always draw a diagram with electromagnetism questions, they are usually very geometry based.

Then work out the force per unit volume at radius r, and then you can use the fact that it is in equilibrium so the pressure must match this force.

X-men ?

OP

TableChair

Right how far have you got?

First draw a diagram of it. Always draw a diagram with electromagnetism questions, they are usually very geometry based.

Then work out the force per unit volume at radius r, and then you can use the fact that it is in equilibrium so the pressure must match this force.

Done all that....didnt get very far.

Tried to use forces between parallel currents...didn't get far with that either.

Can work out Magnetic field for any radius r inside the cylinder...but dont know how that helps.

Force per unit volume would be nice....if I can figure out how to work out the force.

Basically...I havent really gotten anywhere...I don't really know how to approach the quesiton, so if anyone could point me in the right direction regarding which laws to use etc, would be helpful

Reply 4

TableChair

1

Plutoniummatt

Done all that....didnt get very far.

Tried to use forces between parallel currents...didn't get far with that either.

Can work out Magnetic field for any radius r inside the cylinder...but dont know how that helps.

Force per unit volume would be nice....if I can figure out how to work out the force.

Basically...I havent really gotten anywhere...I don't really know how to approach the quesiton, so if anyone could point me in the right direction regarding which laws to use etc, would be helpful

Ok. So consider a small volume and work out the force on it from the field. You know the current through it, and you know the field, so you can work out the force.

Reply 5

Kyle_S-C

12

TableChair

Ok. So consider a small volume and work out the force on it from the field. You know the current through it, and you know the field, so you can work out the force.

It's weird when you help people. I'm kinda scared...

Reply 6

Plutoniummatt

OP

8

TableChair

Ok. So consider a small volume and work out the force on it from the field. You know the current through it, and you know the field, so you can work out the force.