Question

The figure below shows a bar of mass m = 0.240 kg that can slide without friction on a pair of rails separated by a distance = 1.20 m and located on an inclined plane that makes an angle θ = 29.0° with respect to the ground. The resistance of the resistor is R = 2.20 Ω and a uniform magnetic field of magnitude B = 0.500 T is directed downward, perpendicular to the ground, over the entire region through which the bar moves. With what constant speed v does the bar slide along the rails?

Answer 1

    

   Angle between B and v   φ   =   90 - 29   =   61⁰

   Force exerted due to magnetic field   F   =   B * I * L * sin φ

                                                                  =   B * (V / R) * L * sin φ

   since induced EMF   V   =   B * v * L * sin φ

   F   =   B * ( B * v * L * sin φ / R) * L * sin φ   =   B² * v * L² * sin² φ / R   

   When the bar slides at constant speed, net force on it must be zero, i.e.

   m * g * sin θ   =    B² * v * L² * sin² φ / R

   0.240 * 9.8 * sin 29⁰   =   0.500² * v * 1.20² * sin² 61⁰ / 2.20

   speed of bar      v   =   1.14 * 2.20 / 0.275

                                 =   9.11      m/s