Question 3.7.1: Compute the force on a wire carrying a current i above a fer...

Compute the force on a wire carrying a current i above a ferromagnetic plate as shown in Fig. 3.43a. Assume that the plate has an infinite permeability μ ≈ ∞.

3.7.1
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We replace the plate by an image current as shown in Fig. 3.43b. The problem reduces to finding the force between two parallel wires carrying a current i and separated by a distance 2h. This was solved in Example 3.2.7 and the force is given by Eq. (3.53) with d = 2h

Eq. (3.53): F = – \frac{μ_{0}I_{1}I_{2}}{4πd}.\hat{y}

F = – \frac{μ_{0}i^{2}}{4πh}\hat{z}.                (3.302)

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