Question

An electron is accelerated from rest through a potential difference of magnitude V between infinite parallel plates P₁ and P₂. The electron then passes into a region of uniform magnetic field strength B which exists everywhere to the right of plate P₂. The magnetic field is directed into the page.

(a). On the diagram above, clearly indicate the direction of the electric field between the plates.

(b). In terms of V and the electron’s mass and charge, determine the electron's speed when it reaches plate P₂.

(c). Describe in detail the motion of the electron through the magnetic field and explain why the electron moves this way.

(d). If the magnetic field remains unchanged, what could be done to cause the electron to follow a straight-line path to the right of plate P₂?

Answer 1

  (a) The E field points left since it’s a negative charge and is moved opposite the E field.

(b) Work done by the accelerating plate = kinetic energy gained. W = K … Vq = ½ mv² … v = √ (2Ve/m)

(c) Using the LHR, the force on the electron would be down when it enters the B field. This will turn the charge and the resulting B force will act as a centripetal force making the charge circle.

(d) Using an E field to create a force equal and opposite to the F_b could make the charge move in a straight line. Since the charge is negative and the initial F_b is down, The E field would point down to make an upwards F_e .