Peoples Physics Book Version-3

http://www.ck12.org Chapter 14. Magnetism

Example 2: Circular Motion in Magnetic Fields

Consider the following problem: a positively charged particle with an initial velocity of~v 1 , chargeqand massm
traveling in the plane of this page enters a region with a constant magnetic field~Bpointing into the page. We are
interested in finding the trajectory of this particle.

Since the force on a charged particle in a magnetic field is always perpendicular to both its velocity vector and the
field vector (check this using the second right hand rule above), aconstantmagnetic field will provide a centripetal
force — that is, a constant force that is always directed perpendicular to the direction of motion. Two such
force/velocity combinations are illustrated above. According to our study of rotational motion, this implies that
as long as the particle does not leave the region of the magnetic field, it will travel in a circle. To find the radius of
the circle, we set the magnitude of the centripetal force equal to the magnitude of the magnetic force and solve forr:

Fc=

mv^2

r

=FB=qvBsinθ=qvB

Therefore,

r=

mv^2

qvB

In the examples above,θwas conveniently 90 degrees, which made sinθ=1. But that does not really matter; in
a constant magnetic fields a differentθwill simply decrease the force by a constant factor and will not change the
qualitative behavior of the particle, sinceθcannot change due to such a magnetic force.(Why? Hint: what is the
force perpendicular to? Read the paragraph above.)

Magnetism Problem Set

1. Can you set a resting electron into motion with a stationary magnetic field? With an electric field? Explain.


2. How is electrical energy produced in a dam using a hydroelectric generator? Explain in a short essay involving
   as many different ideas from physics as you need.


3. A speaker consists of a diaphragm (a flat plate), which is attached to a magnet. A coil of wire surrounds the
   magnet. How can an electrical current be transformed into sound? Why is a coil better than a single loop? If
   you want to make music, what should you do to the current?