Electrodynamics: Motion of charges in a magnetic field Basics

1. Electrodynamics: Motion of charges in a magnetic field Basics • OK, we know • A current (moving charges) creates a magnetic field, and • A changing magnetic field induces a current • What happens when a charge passes through a magnetic field? • If the charge is moving parallel to the magnetic field lines, it experiences no force. • If the charge is moving perpendicular to the field lines, it experiences a force. • Consider what happens in a solenoid. We thought of this in terms of interacting magnetic fields. A current through the solenoid creates a magnetic field that can either attract or repel a permanent magnetic. We also used this concept to explain how a motor worked. • We can also look at this as charge moving in a magnetic field. The consequence (attraction or repulsion is the same).

2. Electrodynamics: Motion of charges in a magnetic field Basics The ‘right hand rule’ helps determine the direction of force.

3. Electrodynamics: Motion of charges in a magnetic field Hall effect Current flows in the same direction in both diagrams. In the top picture, the electrons are moving (opposite the current I). These moving charges experience a force to the left and charge the left side negatively with respect to the right side. In the bottom picture, positive charges moving in the direction of I experience a force to the left, yielding the opposite voltage. This is how Rowland and Hall found that in metals, it is the electrons that move.

4. + – 1 2 + + d Electrodynamics: Motion of charges in a magnetic field Mass spectrometry Lorentz equation: F = qE + qv×B From electrostatics, an ion at position 1 has a potential energy of PE = qV relative to position 2. As the particle moves from 1 to 2, the potential energy is converted to kinetic energy qV = ½ mv2. Particles of the same charge but different masses will have different velocities exiting the accelerator. Particles having the same mass but different charges will likewise have different velocities: more highly charged particles will be traveling faster because the potential energy is larger. So we need to separate particles both by velocity and by mass.

5. + – 1 2 + + d Electrodynamics: Motion of charges in a magnetic field Mass spectrometry Lorentz equation: F = qE + qv×B In the velocity selector, charged particles are acted on by both electric and magnetic fields. The electric field will push a +1 charged ion down toward the negative plate with a force FE = qE, where E is the electric field (V/d) in the selector. The magnetic field is going into the page. A positive charge moving perpendicular to a magnetic field will experience a force FB = qv×Bupward (refer to slide 2). We can tune the electric and magnetic field such that the net force on a particle is zero, and the particle travels straight through. This is when FE = FB . Thus, a particle with velocity v = E/B will travel straight through, and particles with other velocities will move upward or downward as shown.

6. Electrodynamics: Motion of charges in a magnetic field Mass spectrometry Lorentz equation: F = qE + qv×B + – 1 2 + + + d + + From the PE = KE equation for the accelerator, we know that v = (2qV/m)½ So a particle having twice the mass and twice the charge will have the same velocity. Now that we have particles all the same velocity, we need to separate them on the basis of mass. Positively charged particles traveling in a magnetic field pointing out of the page will experience a force perpendicular to the direction they are traveling. The force F = vB on the particle as it moves through the field is as shown, and the particle begins to spiral. Note that all particles experience the same force because v is the same and B is unchanging! However, from Newton’s law F = ma, and particles of different mass will have different accelerations (different curved trajectories). Thus lower mass particles will be accelerated more strongly, and will have a tighter curve.

7. Electrodynamics: Transistors BJT (bipolar junction transistor) A transistor acts as a gate. Electrical print symbol of a NPN transistor When a sufficiently high voltage is applied to terminal B, the resistance across C and E becomes smaller. In this way a transistor can act as a switch or Boolean logic element (open/closed or on/off) Hydraulic equivalent to a transistor. With sufficient pressure applied to B, fluid will flow from C to E.