Centripetal force on charges in magnetic fields

Which way does a particle get pushed if the the magnetic field is is always perpendicular to the

direction of travel ?

• No mater which way the charged particle turns the force on it is always perpendicular to its motion.

Circular motion -the force is always perpendicular to the direction of travel

-negatively charged particle-magnetic field into the-magnetic force is perpendicular to the velocity, and so velocity changes in direction but not magnitude. Uniform circular motion results.

electron moving at right angles to a uniform magnetic field.

• Circular motion

• F = mv2 / r

• F force (Newton, N)• m mass ( Kg)• v velocity (m/s)

• B magnetic field• q charge

• Force on a charge particle in a magnetic field

• F = qvB sinθ

• v perpendicular to B:• F = qvB

• qvB = mv2 / r

• r = mv/ q B

• r = mv/ q B

• Gives you the radius of a charge particles path in a magnetic field, given its mass and velocity.

Relationship between radius and magnetic field, mass and velocity

r = mv/ q B• Magnetic field B: The stronger the magnetic field, the

stronger the force– and therefore the smaller the radius of the charge

• Velocity v: the more speed a charged particles has, the harder it is for the magnetic field to corral ( circle) the particle, and so it travels in a circle with a bigger radius.

• Mass m: the more mass the charged particle has, the harder it’ll be to bend its path, sot the more mass, the bigger the radius of the circle travels in.

• If the velocity of the electron is due to its having been accelerated through a potential difference of magnitude V (volts), then the kinetic energy of the electron is

• ½ mv2 = qV

• write for the charge to mass ratio of the electron

q/m = 2V / B2r2

Example

• Alpha particles of charge q = +2e and mass m = 6.6 x10-27 kg are emitted from a radioactive source at a speed of 1.6 x 10 7 m/s. What magnetic field strength would be required to bend these these in a circular path of radius r = .25 m?

• e = 1.6 × 10-19

Alpha particles of charge q = +2e and mass m = 6.6 x10-27 kg are emitted from a radioactive source at a speed of 1.6 x 10 7 m/s. What magnetic field strength would

be required to bend these these in a circular path of radius r = .25 m?e = 1.6 × 10-19

• Set the force on the particle due to the magnetic field equal to centripetal force necessary to keep the particle moving in a circle.

• qvb = mv2/r• cancel the v's where possible• qB = mv/r• B = (mv)/(qr)• = (6.6 x10-27 * 1.6 x107)/(2e * .25)• = 1.32 T

Example

• A singly charged positive ion has a mass of 2.5 x 10-26 kg. After being accelerated through a potential difference of 250 V, the ion enters a magnetic field of 0.5 T, in a direction perpendicular to the field. Calculate the radius of the path of the ion in the field

A charged positive ion has a mass of 2.5 x 10-26 kg. After being accelerated through a potential difference of 250 V, the ion enters a magnetic field of 0.5 T, in a direction perpendicular to the field. Calculate the radius of the

path of the ion in the field

56,568 m/s

0.0177 m

We need to solve for the velocity!