Advertisements
Advertisements
Question
Figure shows a rectangular loop conducting PQRS in which the arm PQ is free to move. A uniform magnetic field acts in the direction perpendicular to the plane of the loop. Arm PQ is moved with a velocity v towards the arm Rs. Assuming that the arms QR, RS and SP have negligible resistances and the moving arm PQ has the resistance r, obtain the expression for (i) the current in the loop (ii) the force and (iii) the power required to move the arm PQ.
Advertisements
Solution
Let the length RQ = x and RS = l.
Let the magnitude of the uniform magnetic field be B.
(a) The magnetic flux Φ enclosed by the loop PQRS is given by,Φ=BIx
As, x is changing with time, the rate of change of flux Φ will induce an emf given by:
`E = - (dphi)/dt = -(d(BIx))/dt`
`-BI dx/dt = Blv [as,dx/dt = -v]`
Current in the loop is given by,
`a = E/r = (BIv)/r`
(b) The magnetic force on the PQ is,
`F = BII = B((BIv)/r) xx I (B^2I^2v)/r`
(c) Power required to move the arm PQ is, `p = Fxx V = (B^2I^2V)/r xx v =(B^2I^2V^2)/r`
APPEARS IN
RELATED QUESTIONS
A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil?
A metallic loop is placed in a nonuniform magnetic field. Will an emf be induced in the loop?
Calculate magnetic flux density of the magnetic field at the centre of a circular coil of 50 turns, having a radius of 0.5m and carrying a current of 5 A.
The magnetic flux linked with the coil (in Weber) is given by the equation- Փ = 5t2 + 3t + 16. The induced EMF in the coil at time, t = 4 will be ______.
The magnetic flux linked with a coil in Wb is given by the equation Φ = 3t2 + 4t + 9. Then the magnitude of induced emf at t = 2 sec will be ______.
The unit of magnetic flux in SI is ______
A loop, made of straight edges has six corners at A(0, 0, 0), B(L, O, 0) C(L, L, 0), D(0, L, 0) E(0, L, L) and F(0, 0, L). A magnetic field `B = B_o(hati + hatk)`T is present in the region. The flux passing through the loop ABCDEFA (in that order) is ______.
A circular coil of 1000 turns each with area 1 m2 is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of 0.07T. The maximum voltage generation will be ______ V.
A circular coil has radius ‘r', number of turns ‘N’ and carries a current ‘I’. Magnetic flux density ‘B’ at its centre is ______.
What is the flux when the magnetic field is at an angle \[\theta\] to the area vector?
