What is the relationship between a force field and a potential field?

[bert2002]

Homework Statement

[/B]
I have been given an equation for the magnetic potential of a buried magnetic object which is as follows

P_m=α/x²

Where α is some constant and x is the distance from the magnetic body.
I need to derive an expression for the magnetic field strength at some distance x away from the magnetic body.

The Attempt at a Solution

I know that the magnetic body will generate it's own magnetic field which in essence is a vector field of magnetic force lines. My question Is, is deriving an expression for the magnetic field strength simply a case of integrating the expression for the magnetic potential with respect to the position x ? If not how do I go about solving this problem ?

Thanks in advance.

 

[Ray Vickson]

Homework Statement

[/B]
I have been given an equation for the magnetic potential of a buried magnetic object which is as follows

P_m=α/x²

Where α is some constant and x is the distance from the magnetic body.
I need to derive an expression for the magnetic field strength at some distance x away from the magnetic body.

The Attempt at a Solution

I know that the magnetic body will generate it's own magnetic field which in essence is a vector field of magnetic force lines. My question Is, is deriving an expression for the magnetic field strength simply a case of integrating the expression for the magnetic potential with respect to the position x ? If not how do I go about solving this problem ?

Thanks in advance.

What is the relationship between a force field and the potential field? (This is well explained in many sources, both in book form and on-line.)

 

[bert2002]

What is the relationship between a force field and the potential field? (This is well explained in many sources, both in book form and on-line.)

I'm pretty rusty with this material it's been a while. A potential field is a scalar field and a force field is a vector field, so in finding the force do I take the gradient of the potential and split r into its 3 dimensional components ?