Question

A particle having mass 0.5kg and charge 0.2C is projected with a speed $V_0$ = 10 m/s from the periphery of a circle of radius R = 5m towards the centre as shown in the figure such that region inside the circle carries a uniform magnetic field of strength $B_0$ = 5T into the plane and in the outside region has a uniform magnetic field of the same strength coming out of the plane then, (Assume the center O to be the origin of the co-ordinate axis)

• A. the motion of the charged particle is periodic
• B. the particle crosses line AB after nearly 5.1 s of its start from the periphery
• C. the force on the charged particle due to uniform magnetic field is 20 N
• D. the co-ordinates of the center of the circle at t = 2s is (5, 5)

Answer 1

Answer: (A), (B)

the motion of the charged particle is periodic, the particle crosses line AB after nearly 5.1 s of its start from the periphery

Answer 2

The motion of the charged particle is a sequence of circular arcs in the regions with different magnetic fields. Due to the specific parameters and geometry, the path is closed and the particle returns to its initial state, making the motion periodic. The period is calculated to be $\pi$ seconds. Assuming the line AB is given by $y=-x$, the particle crosses this line at specific times. By calculating the crossing times, we find that one of the crossings occurs at approximately 5.1 seconds from the start. The force on the charged particle is constant in magnitude and equal to $|q|V_0 B_0 = 10$ N. The center of the circular path is always at (-5, 5).