Physics · Moving Charges And Magnetism · NEET
The magnetic force F = qvB is always perpendicular to the velocity. A force that stays at 90 degrees to motion can never change the speed, only the direction. A constant-magnitude force that is always sideways is exactly what makes an object turn in a circle. So the magnetic force acts as the centripetal force and the path is a circle.
No. Speed stays constant. Because the force is always perpendicular to velocity, the magnetic force does zero work (W = F.d = 0 when angle is 90 degrees). No work means no change in kinetic energy, so the speed and the kinetic energy stay exactly the same. Only the direction of velocity keeps changing.
The magnetic force itself is the centripetal force. Set qvB = mv^2/r. Cancel one v: qB = mv/r, so r = mv/qB. There is no extra string or gravity involved; the magnetic force alone bends the path.
T = 2πm/qB has no v in it. A faster particle moves on a bigger circle (larger r), but it also covers that bigger circle faster. The two effects cancel exactly, so every particle of the same q and m takes the same time for one loop. This is the key idea behind the cyclotron.
Then the angle between v and B is 0, so F = qvB sin0 = 0. The magnetic force is zero and the particle moves in a straight line at constant speed. Circular motion needs the velocity to have a component perpendicular to B. If it is at some other angle, you get a helix.
An electron is moving in a circular path under the influence of a transverse magnetic field of 3.57 x 10^-2 T. If the value of e/m is 1.76 x 10^11 C/kg, the frequency of revolution of the electron is:
Ionized hydrogen atoms and alpha-particles with same momenta enter perpendicular to a constant magnetic field B. The ratio of the radii of their paths rH : r_alpha will be:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
r = mv/qB, where m is mass, v is speed, q is charge and B is the magnetic field. A heavier or faster particle makes a bigger circle; a stronger field or bigger charge makes a tighter circle.
Time period T = 2πm/qB and frequency f = qB/(2πm). Both depend only on q, m and B, never on the speed of the particle.
No. The magnetic force does no work, so kinetic energy and speed stay constant. Only the direction of velocity changes.
Use the right hand rule (or F = qv x B) to find the force direction. For a positive charge, point fingers along v, curl towards B; the thumb gives the force, which points to the centre of the circle. For an electron (negative), the force is opposite.
When the velocity is at an angle to B (not exactly 90 degrees). The parallel component of velocity is unaffected and carries the particle forward, while the perpendicular component makes it circle, giving a helical path.
