(a) A metallic rod of length l is moved perpendicular to its length with velocity v in a magnetic field `vec(B)` acting perpendicular to the plane in which rod moves. Derive the expression for the inducced emf.
(b) A wheel with 15 metallic spokes each 60 cm long, is rotated at 360 rev/min in a plane normal to the horizontal component of earth's magnetic field. The angle of dip at that place is `60^(@)`. If the emf induced between rim of the wheel and the axle is 400 mV, calculate the horizontal component of earth's magnetic field at the place.
How will the induced emf change, if the number of spokes is increased ?

Explanation

(a) Let the conductor PQ of length = l, move freely in a uniform magnetic field `vec(B)`. Let any arbitrary charge q also move in the circuit with same velocity.
Lorentz Force = `F_(m) = Bqv`
WD in moving charge from P to Q = `W = F_(m) xx L`
`w = qv Bl`
Now, `epsi = (wD)/(q) = (qvBl)/(q) or epsi = Blv`
(b) `l = 60 xx 10^(-2) m`
`v = 400 xx 10^(-3)v`
`rArr (400 xx 10^(-3) xx 2)/(12pi xx 60 xx 0 xx 10^(-4))`
So `w = 360 xx (2pi)/(60) = 12pi` rad/sec
Induced emf `= (Bwl^(2))/(2) = V = (B_(H) wL^(2))/(2)`
`rArr V = (5.89 xx 10) T`