# Prove that the magnetic field at the centre of the sphere is zero when____

1. Oct 9, 2012

### lindloda

A metallic sphere of radius R and specific resistance ρ is taken and two wires( negligible resistance) connected to it at random positions (say at an angle θ apart from each other.both the wires are perpendicular to the surface of the metallic sphere. Prove that the Magnetic field B at the centre O is zero when a current I is turned on in the circuit.

This situation is kind of like -
imagine a hollow pendulum . now its connected to one thread(suppose its a wire.) ...we connect another wire to this pendulum at a random position. and using a cell create a potential difference between the two ends of the wires such that a current flows through the wires, into the sphere ...all around the sphere and back to the other wire

What I did is assume to the sphere to be made of two different resistors connected in parallel. one piece subtends a solid angle dΩ at the centre and hence the other piece will subtend an angle 4∏- dΩ.
After that ...I have no clue.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: Oct 9, 2012
2. Oct 9, 2012

### rude man

Hints for you:

1. supposing the connections were made at 180 deg apart, like north & south poles, what would be the mag field at the center of the sphere?

2. Now assume the connections are made randomly. What can you say about the current density (amp/m2) in any direction but passing thru the center, compared to the current density of 1 above?

3. Oct 10, 2012

### lindloda

I know its really easy for north and south pole like situation, but

4. Oct 10, 2012

### rude man

Well, what do you conclude is the B field at the center of the sphere when the connections are made to 180 deg. opposite poles, and what is your rationale?

5. Oct 12, 2012

### lindloda

Are you serious ?

I know it's OBVIOUSLY ZERO for any position.

And then as a mental exercise I invite you to think what does "Prove the mgn. field is zero" means ..

[Hint:
It means the magnetic field IS ZERO !]

I know it is zero.
I just need the solution .
I cant find it anywhere.

I hate to be rude but
I dont need cross questioning ..
All I want is the solution.

6. Oct 12, 2012

### rude man

If it's OBVIOUSLY zero for any position then you must know WHY it's obvious! Saying I know it's zero because my prof says so is not proving it.

I suggest showing mathematically that the B field is zero along the axis connecting contact points 180 deg. apart, then follow up with an argument why it should apply to any two connections.

7. Oct 12, 2012