# I Forces Between 2 large conductors

1. Jul 23, 2016

### JasonM

If I have two large cunducting bars (not the same size) that are separated by a distance D but connected with another conductor in between creating a "U" shape and apply a large current through it, how can I calculate the magnetic forces between the two large ends of the "U" shape?

I have already looked at it as two conductors parallel to one another (looking past the fact that they are connected) and came up with some numbers for the mag field and force between them. The forces should always be repelling the bars apart from one another in this case as it is single phase AC current in the shape of a "U".

I am just trying to find what type of reinforcement I need between them in order for them to not blow apart when I exert a very high current through the system.

2. Jul 24, 2016

### Delta²

The magnetic field from one conductor (No1)$B_1$ at the line where the other conductor (No2) lies will have the same value across all points of line and it will be

$B_1=\frac{\mu_0}{2\pi}\frac{I}{D}$

Hence it will exert a laplace force $F_{12}=B_1Il=\frac{\mu_0}{2\pi}I^2\frac{l}{D}$ where l the length of conductor.

To calculate the current I, you 'll probably have to take into account the self inductance of the whole circuit (unless you using an ampermeter to measure directly the current). According to some formula a good approximate value for the self inductance of such a circuit is

$$L=4\mu_0l(log\frac{D}{r}+\frac{\mu}{4})$$

where r the radius of each conductor and $\mu$ the permeability of the conductors. This result is a good approximation if the distance D is much smaller than the length l.

Last edited: Jul 24, 2016
3. Jul 24, 2016

### JasonM

I know the current I will be putting through it. So it really is as simple as the formula above for calculating the force they have on each other?

Will the small part of the U that is connecting the bars have enough force to impact or should I look at it as just a bracing between the two conductors?

4. Jul 24, 2016

### Delta²

Well the formula for the force is also an approximation but it is a very good approximation if the distance D is much smaller than the length L.

I believe same rule applies here, that is if the total length of the U part is much smaller than the length L, then the force from the U part will be negligible in comparison with the force from the straight L part.