A positron initially moving through empty space at a constan

A positron initially moving through empty space at a constant velocity of V_0 = 1.0 times 10^5 m/s j, approaches the origin along the negative y axis. As it passes through the origin, it suddenly experiences a magnetic field; for all y > 0, the magnetic field is B = B_0 i, where B_0 = 1.0 mT; for all y0? (c) How much time passes before the positron reemerges in the domain for which y

Solution

We know that a charged particle moving in a magnetic field suffers a force given as:

F = q V x B and the direction of the force is same as the direction of the cross product of the velocity and the magnetic field.

We will use the above to solve the given problems as follows:

a.) Once the positron enters the magnetic field, it will be acted upon by a force given as: F = eVoBo

This force will make the positron go along a curve into the page such that the centripetal force will be provided by the magnetic force acting on the positron.

Hence we can balance the centripetal force with the magnetic force to get:

eVoBo = mVo²/R

or, R = mVo / eBo = 9.1094 × 10^-31 x10^5/ 10^-3 x 1.6022 × 10^-19 = 5.6856 x 10^-4 m

Therefore the radius of curvature of the positron in the region y > 0 is 5.6856 x 10^-4 m

Part b.) As the positron moves around a curve lying in the plane x = 0, it will emerge at a point 2R away from the origin along the -z direction. Also the x and y coordinates will be zero as the positron goes around a semi circle and emerges near the z axis only.

That is the coordinate of the point would be: (0 , 0, -11.37 x 10^-4 )

Now the positron goes around a curve of length Pi x R with velocity Vo

Hence the time taken = Distance / Speed = 17.853 x 10^-4 / 10^5 = 17.853 x 10^-9 seconds