A long vertical wire carries a steady 15 A current. A pair of rails are horizont

Question

A long vertical wire carries a steady 15 A current. A pair of rails are horizontal and are 0.3 m apart. A 14.6 ? resistor connects points a and b, at the end of the rails. A bar is in contact with the rails, and is moved by an external force with a constant velocity of 0.5 m/s as shown. The bar and the rails have negligible resistance. At a given instant t1, the bar is 0.1 m from the wire, as shown. In Figure, at time t1, the induced current in

A long vertical wire carries a steady 15 A current. A pair of rails are horizontal and are 0.3 m apart. A 14.6 Ohm resistor connects points a and b, at the end of the rails. A bar is in contact with the rails, and is moved by an external force with a constant velocity of 0.5 m/s as shown. The bar and the rails have negligible resistance. At a given instant t1, the bar is 0.1 m from the wire, as shown. In Figure, at time t1, the induced current in mu A is: Express the answer in three decimal places.

Explanation / Answer

V = d(fi)/dt

= d(B.A)/dt

= (mu*I/2pi*r)*L*(2-r)/dt

= (mu*I/2pi)*L*d((2-r)/r)/dt

=(mu*I/2pi)*L*2/r^2*dr/dt

= (mu*I/2pi)*L*2/r^2*v

= (mu*I*v*L*/pi*r^2)

= 4*10^-7*15*0.5*0.3/0.1^2

= 0.00009 V

I = v/R

= 0.00009/14.6

= 6.16 uA

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