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Two parallel, long, straight conductor l...

Two parallel, long, straight conductor lie on a smooth plane surface. Two other parallel so as to form a square of side a initially. A uniform magnetic field `B` exists at right angles to the plane containing the cinductors. Now they start moving out with a constant velocity `v`.
(A) Will the induced emf be time dependent?
(b) Will the current be time dependent ?

Text Solution

Verified by Experts

The correct Answer is:
(a) Yes; (b) No
(a) suppose the magnetic field is into the plane of the page.

after time `t`, the length of each side of the square is `l = a + 2vt`
area of square,
`l^(2) = (a + 2 vt)^(2)`
`= (a^(2) + 4v^(2)t^(2) + 4avt)`
`phi = Bl^(2) = Ba^(2) + 4Bv^(2)t^(2) + 4ba vt`
`|epsilon| = (dphi)/(dt) = 8Bv^(2)t + 4B va = 4Bv(2 vt + a)`
Hence, emf is time-dependent.
(b) The emf and resistance both are time dependent, but at any time `t` the resistance of loop is `R = 4mu(a + 2vt)`, where `mu` is resistance per unit length of wire
`rarr` `i = (4Bv(a + 2vt))/(4mu(a + 2vt)) = (Bv)/(mu) constant`
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