Physics II PHY 202/222 Magnetism 452 South Anderson Road Rock Hill, SC 29730 www.yorktech.com

Magnetism– Test 5 SP: 3 Beiser Chapters 27 MC: odd, SP: 5 – 17 odd Browne Chapter 26-29 for PHY 222 Students 26: 1,5,9 27: 2, 28: 7 29: 1, 2

Chapter 27 – Magnetism Beiser p.319

Magnets When we think of magnets we either consider permanent magnets or magnetic effects of moving charge. Since permanent magnets come from moving charge, we consider moving charge first. Beiser p.319

Magnetic Fields Unit of magnetic field is the Tesla where 1 T = 1 N/Am = 1 Weber/m2 = 10,000 Gauss The field around a strong permanent magnet is 0.1 T. An MRI is from 0.2 to 1.5 T. A junkyard electromagnet for lifting cars is 1 T. Beiser p.319

Magnetic Field of a Straight Current Every current in a wire generates a magnetic field. Point the thumb of your right hand in the direction of the current, and your curled fingers will point in the direction of the field. The magnitude at a distance s from the wire is given by the formula: Beiser p.320

Magnetic Field of a Loop A current in a loop of wire generates a magnetic field. Point the fingers of your right hand in the direction of the current, and your thumb will point in the direction of the field inside the coil. The magnitude of the field inside the loop is given by the formula: Beiser p.321

Earth Magnetism The Earth has a magnetic field due to currents of molten material in the core. The magnitude is around 3 x 10 -5 T Beiser p.322

Magnetic Force on a Moving Charge A charge Q moving in a magnetic field B with velocity v will experience force F. In the picture, the charge is moving to the right in a magnetic field into the screen. The magnitude of the force is given by The force will be upwards as follows: Put the thumb of your right hand in the direction of v. Put your fingers in the direction of B. Curl fingers up. Force will be in direction of fingers for a positve charge, and opposite for a negative charge. v Magnetic field into screen F B +Q Beiser p.323

Magnetic Force on a Current v Magnetic field into screen F B Wire +Q I L – Length of wire in magnetic field F = I L B The force will be upwards as follows: Put the thumb of your right hand in the direction of I. Put your fingers in the direction of B. Curl fingers up. Force will be in direction of fingers. Beiser p.323

Force Between two Currents L s If currents are in opposite directions, the force is repulsive; same attractive. Beiser p.324

Ferromagnetism Beiser p.327

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Chapter 28 – Electromagnetic Induction Beiser p.335

Electromagnetic Induction A current is produced if: If a conductor is moved in a magnetic field If a magnet is moved near a wire, especially a coil of wire A magnetic field changes near a conductor/coil. For a straight conductor moving perpendicular to a magnetic field. Beiser p.335

Faraday’s Law For a magnet moving in a coil: Lenz’s Law: an induced current is always in the direction so that it’s own magnetic field opposes the effect that created it. Hence the negative sign above. Beiser p.335,6

Transformers N1 N2 Beiser p.337

Self Induction A change in current in a conductor causes a change in magnetic field. A change in magnetic field causes an self-induced emf. Where L is the inductance of the circuit component. For a solenoid: Beiser p.339

Inductors in Combination

Energy of an Inductor Beiser p.341

Time Constants and Current When a switch in an inductive circuit is closed, the current builds up to it’s full value according to the formula: Where the time constant, T = L / R. Beiser p.341-3

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Chapter 29 – Alternating Current Circuits Beiser p.350

Alternating Current V = constant V = Vmax sin ωt I= Imax sin ωt AC Alternating Current V = Vmax sin ωt I= Imax sin ωt DC Direct Current V = constant Beiser p.350

Generators Split ring commutator Slip rings Generator: Move the coil, electricity out. Motor: Electricity in, motion out.

Effective Values Since the average AC voltage V = Vmax sin ωt is zero, we need a way to be able to calculate its capacity to do work. So we use the “effective value” or root-mean-square (rms) value. Beiser p.350

Phase Angle ELI – ICE In an AC circuit with only an inductor (L) the voltage (E) leads the (I) current by 900. In an AC circuit with only an capacitor (C) the current (I) leads the voltage (E) by 900. In AC circuits with both inductors and capacitors you would have to find the phase angle as shown in the book. Beiser p.353

Maxwell’s Equations Gauss’s Law for electricity: Electric fields come from charges Gauss’s Law for Magnetism: There are no magnetic charges/monopoles. Any “ball” has the same B out as in: sum =0 Faraday’s Law: Change in magnetic field makes electricity. Ampere’s Law: Change in electric field makes magnetism. ΔE → ΔB → ΔE → … propagates through space as light or other EM waves. WOW! Browne p.343