Question

What pressure does the lateral surface of a long straight solenoid with n turns per unit length experience when a current I flows through it?

Answer 1

When self-forces are involved, a typical factor of 1/2 comes into play. For example, the force on a current carrying straight wire in a magnetic induction B is BIl. If the magnetic induction B is due to the current itself then the force can be written as,

In the present case, B(I) = μ₀nI and this acts on nl ampere turns per unit length, so,