A matel wire PQ of mass 10g lies at rest on two horizontal metal rails separated by 4.90 cm . A vertically downward magnetic field of magnitude 0.800 T exists in the space. The resistance of the circuit is slowly decreased and it is found that when the resistance goes below`20.0 Omega`, the wire PQ starts sliding on the rails. Find the coefficient of friction.

Explanation

(a) When resistance `R = 20 Omega`
Current in the wire `i = (E)/(R ) = (6)/(20) = 0.3 A`
Magnetic force on wire `F_(m) = Bil`
The wire is about to move.
If `F_(m) ge f_(max)`
`Bil ge mu mg`
`mu = (Bil)/(mg) = (0.8 xx 0.3 xx 5 xx 10^(-2))/(10 xx 10^(-3) xx 10)`
`= 0.12`
(b) When switch `S` is closed, current `i` is established.
Magnetic force on wire `F = Bib`
Acceleration `a = (F)/(m) = (Bib)/(m)`
On the rails:
Velocity of rod after travelling distance `l`
`v^(2) = 2al = (2 Bi bl)/(m)`
On the rough surface:
`F_(m) = 0`
Friction `f = mu mg`
Retardation `a' = (f)/(m) = mu g`
Let wire stops after travelling a distance `d`
`0 = v^(2) - 2a' d`
`d = (v^(2))/(2a') = (2 Bi b l)/(m) .(1)/(2 mu g)`
`= (2 Bi b l)/(2 mu mg) = (Bi b l)/(mu mg) = (Bi l b)/(mu mg)`