Download Understand Ohm`s law in both microscopic

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Understand Ohm’s law in both microscopic ( J   E ) and macroscopic ( V  IR ) form. Have an
understanding of why J and E are related in this way. Given a resistor of cross-sectional area
A and length l, be able to derive the formula R   l / A . Understand what I 2 R means in (ohmic
qV x B force: be able to compute this direction; be able to derive the cyclotron frequency, the
relations between v,  , T, and R for a particle moving in a circle. Be able to correctly get the
sense of revolution of a charge in a given constant magnetic field given the field direction and
the charge of the particle.
F  Idl  B : be able to compute this direction, and understand the meaning of it, e.g. for a
current loop above a magnet.
Biot Savart Law: be able to use to calculate the magnetic field from simple current elements,
e.g. the magnetic field at the center of a circle of radius R carrying current I.
Magnetic dipole moment: what is it, how is it directed, what is its magnitude?
Torque on a magnetic dipole τ  m  B . What does it mean, e.g. what direction does it cause a
compass needle in a background field to rotate, how does it arise, and so on.
Ampere’s Law: be able to find the magnetic field using Ampere’s Law in situations with a high
degree of symmetry. There are a few problems here: planes of current, field inside a solenoid,
problems with cylindrical symmetry.