Answer to Question #181208 in Electricity and Magnetism for Dion Gray

Question

An alpha particle, with velocity of magnitude 500 m/s, travels horizontally into a region of space in which

there is an upward-directed uniform electric field of magnitude 36 N/C and a uniform magnetic field. The

magnetic field makes an angle of 41° with the particle’s velocity vector and is such that it causes the alpha

particle to pass through the region of space undeflected.

Explain how the presence of the magnetic field causes the alpha particle to pass through undeflected beginning with an explanation of what happens to the alpha particle in the presence of the electric field.

Also what will be the magnitude of the magnetic field that is required to cause the alpha particle to pass through undeflected.

Answer 1

The alpha particle is charged particle so it will experience electric force due to the Electric field. The force will be directed along the direction of Electric field only as the alpha particle has positive charge.

Now as the alpha particle is moving, it will experience magnetic force as well due to the magnetic field. If the alpha particle has to go undeflected, then the magnetic force should balance the electric force.

So magnitudes of both the forces will be equal but both will be directed opposite to each other so that net resultant is zero.

Numerically: $F_M = F_E, so \space qVBsin \theta= qE$ F_M = F_E, so qVBsin = qE

$VBsin \theta = E$

So $B = E/Vsin \theta$ , putting values, we get B = 36 ÷ (500 × sin 41) = 0.109746 T