to the magnetic field, then you will need to throw in this extra “sin θ ” term.
Right-hand rule: To find the force on a charged particle.
Point your right hand, with fingers extended, in the direction that the charged particle is traveling.
Then, bend your fingers so that they point in the direction of the magnetic field.• If the particle has a POSITIVE charge, your thumb points in the direction of the force exerted on it.
• If the particle has a NEGATIVE charge, your thumb points opposite the direction of the force exerted
on it.The key to this right-hand rule is to remember the sign of your particle. This next problem illustrates how
important sign can be.
An electron travels through a magnetic field, as shown below. The particle’s initial velocity is 5 × 10^6
m/s, and the magnitude of the magnetic field is 0.4 T. What are the magnitude and direction of the
particle’s acceleration?This is one of those problems where you’re told that the particle is not moving perpendicular to the
magnetic field. So the formula we use to find the magnitude of the force acting on the particle is
F = qvB (sin θ )
F = (1.6 × 10−19 C)(5 × 10^6 m/s)(0.4 T)(sin 30°)
F = 1.6 × 10−13 N.Note that we never plug in the negative signs when calculating force. The negative charge on an electron
will influence the direction of the force, which we will determine in a moment. Now we solve for
acceleration:
Wow, you say ... a bigger acceleration than anything we’ve ever dealt with. Is this unreasonable? After
all, in less than a second the particle would be moving faster than the speed of light, right? The answer is
still reasonable. In this case, the acceleration is perpendicular to the velocity. This means the acceleration
is centripetal , and the particle must move in a circle at constant speed. But even if the particle were
speeding up at this rate, either the acceleration wouldn’t act for very long, or relativistic effects would
prevent the particle from traveling faster than light.