Question

The adjacent figure shows a top view of a bar that can slide on two frictionless rails. The resistance is R = 6.2. A 2.5 T magnetic field is directed perpendicularly downward into the paper. Let l = 1.2 m. (a) Calculate the applied force required to move the bar to the right at a constant speed of 2 m/s. X xx xx x x Bin (b) At what rate is energy delivered to the resistor? app

Answer 1

(a) As the bar moves, a changing magnetic field is created which induces an EMF in the circuit having magnitude (E) = B*l*v; where B is the magnetic field strength, l is the length of the bar and v is the velocity of the bar.

= 2.5*1.2*2 volt

= 6 volt.

The resistance(R) is given as 6 ohm

Therefore, the current induced = E/R

= 6/6 A

= 1 A.

The magnitude of the applied force(Fapp)= iBl sin theta, where theta is the angle between the magnetic field and the length element.

= 1*2.5*1.2*sin(90 degrees)

= 3 N

Thus, the applied force is equal to 3 N towards the right Ans.

(b) The rate at which energy is delivered to the resistor = Power delivered

= E^2/R

= 6^2/6

= 6 J/s or 6 W Ans.