Concepts Of Physics MCQ Edition [Volume 2]PhysicsMagnetic Field
Consider two particles, each of mass m , positioned at a separation distance d inside a uniform magnetic field B . The particles possess opposite charges of equal magnitude q . At an initial time t = 0 , they are projected directly towards one another, each travelling with a speed v . Assume that the Coulomb interaction between the charges is turned off. Let v_m denote the maximum projection speed that allows the par
Options
- AIt moves with a constant speed 2 v_m along a straight line drawn upward in the plane of the figure through the
- BIt moves in a circular path of radius d with a constant speed v_m .
- CIt moves with a constant speed v_m along a straight line drawn upward in the plane of the figure through the p
- DIt comes to rest immediately at the point of collision.
Correct answer
C. It moves with a constant speed v_m along a straight line drawn upward in the plane of the figure through the p
Step-by-step solution
The magnetic force on a moving charge is given by F = q( v B ) . For the particle with charge q moving with velocity v i in a magnetic field -B k , the force is qvB j (upwards). For the particle with charge -q moving with velocity -v i , the force is also qvB j (upwards). Thus, both particles move in circular paths curving upwards. The radius of the circular path is R = mv qB . To just avoid collision, the two circular paths must be tangent to each other. Since the initial separation is d , the sum of their radii m