PhysicsLAB: 2011 B5 Form B

The diagram below illustrates a velocity selector, labeled Region 1. It consists of two parallel conducting plates, with charges on the plates as indicated creating an electric field of magnitude E directed toward the top of the page. A uniform magnetic field of magnitude B₁ directed out of the page exists between the plates. The magnitude of the magnetic field can be adjusted so that only particles of a particular speed pass through the selector in a straight line. A radioactive source to the left of the selector emits charged particles, each having the same charge +q and moving to the right in the plane of the page. The effect of gravity can be neglected throughout the problem.

	(a) i. Derive the equation v = E/B₁ for the speed v of particles that move in a straight line through Region 1.

	(a) ii. Some particles are emitted from the source with speeds greater than E/B₁. Which of the following describes the initial path of one of these particles immediately after entering Region 1? Explain your reasoning.

A constant magnetic field of magnitude B₂ directed into the page is now added in Region 2 to the right of Region 1, as represented in the figure below. Suppose a particle leaves the radioactive source, travels through Region 1 in a straight line, and enters Region 2. For each of the following, express algebraic answers in terms of E, B₁, B₂, q, and fundamental constants, as appropriate.

	(b) Determine an expression for the initial magnetic force on the particle in Region 2 and state its direction.

	(c) Describe the changes, if any, in the magnitude and direction of the magnetic force as the particle moves in Region 2.

	(d) Describe the path of the particle in Region 2.

	(e) Derive an expression for the charge-to-mass ratio q/m of the particle. Specifically note any quantities not previously defined that are included in your answer.