The force is 4.0×10í^5 N and the
chargeq is 2.0 ȝC. What is B?
B = 0.80 T
28.11 - Interactive problem: B field strength and particle motion
In this simulation, you want the magnetic field to exert a force of 1.16×10í^8 newtons
on the positively charged particle. Set the particle’s speed v (the maximum possible
value is 520 m/s) and the magnetic field strength B (the maximum possible value is
3.00 T) to cause the required amount of force, using the controllers provided in the
control panel. You will find that you need to adjust both the speed and the field
strength upward from their initial settings to achieve this force.
If you have any trouble achieving the desired force, review the discussion in the
previous section on determining the strength of a magnetic field. If you have any
questions about how to use the simulation, see the previous interactive problems in
this chapter for complete instructions.28.12 - Physics at work: velocity selector
A velocity selector is a device that allows charged particles moving only at a specified
speed to pass through it. It uses a combination of an electric field and a magnetic field
to “trap” particles moving at other speeds. In addition to being a useful tool, a velocity
selector provides a good way to explore the contrasting effects of electric and magnetic
fields.
To the right is a conceptual diagram of a velocity selector for charged particles. Perhaps
a scientist wants only electrons moving at 50,000 m/s to pass through. The electric field
of the velocity selector points down, and will exert an upward force on an electron.
(Remember that the force is opposite to the direction of the electric field because
electrons are negatively charged.)
A magnetic field is used to counter the effect of the electric field. The magnetic field
strength is set so that the field exerts an equal but opposite force on any electron
moving at 50,000 m/s. Since the force exerted on the electron by the electric field is
upward, the magnetic field force must point down. Electrons with the required speed will
travel horizontally and pass through an aperture at the right end of the selector. Slower
or faster ones will experience a net force and be forced up or down. (We ignore the
force of gravity, whose effect would be minor for a particle moving at this speed.)The sum of the forces on the particle is qE + (qv × B). This equation is called the Lorentz force law. The strength of the electric force equals
|q|E. The strength of the magnetic force equals |q|vB (since the velocity is perpendicular to the field). When the forces sum to zero, these two
expressions are equal in magnitude. On the right, we solve for the speed and see that it equals the ratio of the electric to the magnetic field
strength. As you can see, the charge cancels out.
Can you predict the direction in which this device’s magnetic field needs to point using a right-hand rule? The electric force on the electron
points up, so we want the magnetic field force to point down. Since the charge is negative, the thumb will point in the opposite direction of the
force. This means you want the thumb to point up. The fingers must wrap from the velocity vector to the magnetic field vector. You canVelocity selector
Charges of specific speed pass through
Uses electric and magnetic fields
Electric force balances magnetic force(^514) Copyright 2000-2007 Kinetic Books Co. Chapter 28