Uniform magnetic field 1T directed into the page exists only at positive x as sh

Question

Uniform magnetic field 1T directed into the page exists only at positive x as shown. Proton enters the field with the velocity of 6

Uniform magnetic field 1T directed into the page exists only at positive x as shown. Proton enters the field with the velocity of 6?10 ^6 m/s at 30 degrees to the x-axis (in the plane of the page). Find the distance (d) between the points of entry and exit of the charge to the magnetic field. Find the angle at which charge leaves the magnetic field (with respect to x-axis).

Explanation / Answer

a)

by equating the force

qvB=mv^2/r

r=mv/qB

and

from the figure

particle is entering in the field with theta=30 Degrees w . r. to x axis

and r is radius of the circular path,

then

tangnet line drawn from centre of circular to the pont where the particle is enetering and leaving

also makes the angle theta,

hence

d=r*cos(theta)+r*cos(theta)

=2*r*cos(theta)

=2*mv/qB*cos(theta)

=2*(1.67*10^-27*6*10^6/1.6*10^-19*1)*cos(30)

=1.8825 m

=188.25 cm

b)

here angle made by the tangent line drawn from the center of circular path to the line where the

particle is leaving is 90 derees

hence

requirde theta =90-30

=60 dgrees ..is answer

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