ELECTRICITY & MAGNETISM CHAPTER 8

ELECTRICITY & MAGNETISM CHAPTER 8

E & M - Focus Electric Charge & Force Magnetism Current, Voltage & Power Electromagnetism Simple Electrical Circuits Voltage & Current Transformation

Electric Charge & Force Gravitational Case Electrical Case F g = G m 1m 2 r 2 F e = k q 1q 2 r 2 Only One Kind of Mass + Unlike Charges + - Like Charges +

Electric Current, I Vehicle current Electric current current = kg (mass of vehicles) time current = charge time I = q t amperes = coulombs second

Electric Potential Energy - V Gravitational Case Fg is assumed to be constant Electrical Case Fe is not constant m q1 PE g = wh = mgh w V = W q Fe d h volts = joules coulomb Fe q2

Batteries - Sources of Voltage 1.5V + - q - Move charge q from one battery pole to another. How much work did you do? W = Vq Note that is does not matter what path the charge goes through!

Electrical Resistance - R Conductors support high electric currents because of mobile electrons. Semiconductors have few mobile electrons. Insulators have no mobile electrons. Conductors have low (but not zero) resistance. Semiconductors have high resistance. Insulators have infinite resistance.

Resistance - Gravity Case These guys are doing work against gravity, but their also doing work against friction. h

Electrical Resistance - R Circuit Elements

Electrical Resistance - R R = V I ohms = volts amp R = V I The vulture is above the iguana. I = V R The vulture is above the rabbit. V = IR The iguana and the rabbit are on the same level.

Electrical Power - P Power = Work Time P = W t watts = joules second Recall the equations for I and V I = q t, V = W q and so, rearranging things IV = q t W q = W t = P P = IV

Electrical Power - P From P = IV P = IV And V = IR V R = I We get P = I 2 R P = V 2 R

Simple Electrical Circuits Series Parallel

But First - Gravity! Series water wheels h h1 h2 h3 Key Points: The flow of water through each wheel is the same. The total potential energy drop h = h1 + h2 + h3

But First - Gravity Cw C1 C2 C3 Parallel water wheels h C1 C2 C3 Key Points: Water flow is split unevenly over 3 wheels. Cw = C1 + C2 + C3 The total potential energy drop, h is the same for each wheel.

Series Electrical Circuit We know and so, V = IR V 1 = IR 1 V 2 = IR 2 V 1 + V 2 + V 3 = V = IR 1 + IR 2 + IR 3 V = I ( R 1 + R 2 + R ) 3 V 3 = IR 3 Equivalent series resistance: R eq = R 1 + R 2 + R 3 +...

Parallel Electrical Circuit We know I = V R and I 1 = V R 1 I 2 = V R 2 so, I 1 + I 2 + I 3 = I = V R 1 + V R 2 + V R 3 Equivalent parallel resistance: I = V 1 + 1 + 1 R 1 R 2 R 3 I 3 = V 1 R 3 = 1 + 1 + 1 +... R eq R 1 R 2 R 3

Batteries in Series + 1.5V - + 1.5V - + 1.5V - Total = 4.5 V Batteries in series can supply 3 times the voltage at the same current.

Batteries In Parallel 1.5V + - Batteries in parallel can supply 3 times the current at the same voltage. 1.5V + - 1.5V + - Total = 1.5 V

Magnetite, or Loadstone MAGNETISM Early Magnetite Compass

Gravity, Electric Analogies Gravity Electricity Magnetism Only one kind of mass Attractive only Two kinds of charge, + and - Opposites attract, Like charges repel. There are no magnetic charges, only fields! Opposite poles attract, Like poles repel.

Background - Earth Magnetism Geomagnetism: Magnetite Compass was used for navigation. Paleomagnetism: Most rocks have residual magnetism from the time of their solidification.

The Magnetic Field Thought Experiments: Tiny test compasses could be used to map a magnetic field. Also: You could do this with a test mass to map a gravitational field. You could do this with a test charge to map out and electric field.

Electric Current & Magnetic Field Moving charge creates a magnetic field. I R (wire) + - V Magnetic Field A flow of electric current comes with a magnetic field.

Electric Current & Magnetic Field In a loop, the magnetic field becomes more concentrated at the center. I R (wire) + - V Magnetic Field

Electric Current & Magnetic Field In a coil, the magnetic field becomes even more concentrated at the center. I S + - V R (wire) N Magnetic Field

Right Hand Rule for I If your right thumb points in the direction of conventional current, then your fingers point in the direction of the magnetic field (B-field).

Magnetic Force On Moving Charges Relative motion between the magnetic field and the charge is what counts. For negative charges (electrons) use you left hand. If a conductor is passed though a magnetic field, a current can flow!

Electrical Generation

Changing Magnetic Field A changing magnetic field can also induce electric currents. Output from AC generator on previous slide I I R, load Alternating Magnetic Field This induced current can drive a useful electrical device.

The Transformer Transformers are used to change voltage and current levels in practical power distribution networks. V 2 = N 2 V 1 N 1 I 2 = N 1 V 1 N 2 V Note: Power is conserved P 2 = I 2 V 2 = N 1 I 1 P 2 = P 1 N 2 N 2 N 1 V 2 = I 1 V 1

The Power Grid