Lesson 3.6 - Particle in a Magnetic Field
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RECALL
Force on a particle with charge q in an electric field \( \vec{E}\)
CURRENT IN A CONDUCTOR
When a current flows through a conductor, it represents electrons around the circuit. A current flowing through a conductor generates a magnetic field at right angles to the conductor.
DRAWING CONVENTION
Let's consider a particle travelling through a magnetic field.
The deflection of the charged particle is proportional to
- charge on the particle , q
- velocity of the particle, |v|
- the intensity of the magnetic field, |B|
The deflection is a maximum when the velocity is perpendicular to the magnetic field, \( \theta=90^o \). When it is parallel there is no force acting on it, \( \theta = 0^o\) or \( \theta = 180^o \). So the force on a charged particle of charge q, travelling at v in a magnetic field of |\( \vec{B} \)|
or
where we are taking the cross product of the velocity and the magnetic field, since the force is perpendicular to both.
RIGHT HAND RULE FOR THE CROSS PRODUCT
MAGNETIC FIELD
EXAMPLE PROBLEM #1
What is the force on a \(3.0 \mu C\) charge travelling \(3.0 \times 10^5 m/s \) to the right through a uniform magnetic field of 0.350 T into the page? What about \(-3.0 \mu C\)SOLUTION:
CIRCULAR MOTION
A charged particle in a magnetic field will always be feeling a force perpendicular to its motion. Thus its direction will always be changing and its speed will remain constant. This will generate a circular motion.
WHAT ABOUT A WIRE IN A MAGNETIC FIELD
EXAMPLE PROBLEM #2
A 40cm wire carrying a current of 5.0A is in a 0.50T field facing up. If the wire is at an angle of \(35^o\) from vertical. What is the magnitude of the force on the wire?SOLUTION:
LORENZ FORCE
We can put it all together. Consider a charge, q, travelling at a speed, v, in an electric field, E, and a magnetic field, B. It will feel a force of