The figure below shows the path of a proton (mass m_p, charge +e), as it moves t
ID: 1633493 • Letter: T
Question
The figure below shows the path of a proton (mass m_p, charge +e), as it moves through two regions of magnetic field. It first enters, with speed v, a region of field B_1, wherein its path is half a circle of radius R_1. It leaves region 1, travels a distance d, and enters region 2, where the field has magnitude B_2 and the proton travels in half a circle of radius R_2. (a) Which field is stronger? How can you tell? (b) What are the directions of the two fields? (c) Does the proton spend more time in region 1 or in region 2? (d) Suppose that immediately after the proton leaves region 1 an electric field of magnitude E is applied to it, which is then turned off at the moment it enters region 2. What would be the necessary magnitude and direction of the electric field to produce the trajectories described above, assuming that B_1 = B_2 B?Explanation / Answer
a) Region 2 has stronger field. The reason being, a proton traverses a circular motion of lesser radius in a stronger magnertic field
radius of proton's circular path is given by r = mv/qB
Therefore, higher the magnetic field , B, lesser the radius
b)Region 1 is out of plane of the paper, and region 2 is into the plane of the paper
c)proton spends lesser time in region 2, because the angular velocity of proton is higher in region 2 than in region 1,because it has higher magnetic field. in both the regions, prton travels 180o, and hence higher the anguklar velocity, quicker it travels 180o .