Question

5/6 pts Question 8 An infinite wire and an infinite length conductor sheet are carrying currents 11 and 12, respectively. Both are placed parallel to the the z axis with the wire coinciding with the z axis. The conductor sheet has a semi-circle cross-section with radius b and negligible thickness. Derive an expression for the unit-length force acting on the conductor sheet due to the current passing in the wire. Current / out of the paper Currentl2 into the paper Hint: Start from the equation of the unit-length force acting on an infinite wire due to another infinite wire.

Answer 1

ATLITU solution Crument to into the paper cuorend out of the paper orce d] da bodo let us assume infinites heet is made dx cross section the of and semi-cylindrical infinite lines of Corfinite length And we parallel know that force between this current carrying conductors per unit length F = No Hol I 2 at a distance between conductors

Nature of force is coronents in both for opposite allradive it is same direction of and repulsive In our case and Iz is repulsive. direction of inward. 60, I is outward force would be Now, - dd₂ = 12 (dx) - ab I2 (x do) - I do ab af sinon dfcaso di sino component of be concelled due half Bymo metry: df colll oppose ab dr caro. Net dF - QdF Cogo drsino Boy FE a fof.conso dF - Ho Ildo Ma I Indo 2826 12 Hadj Iz Cosodo 22b - Ho I, I 2 go (ooodoc Madli z +2b to

F - Mo I, I2 A26 net force would be in a dixection F HollI2N