Review Notes AP Physics B Electricity and Magnetism

Electric Fields The electric field around a source charge will be different at different locations around the charge. – Further away from the charge, the magnitude of the force will decrease. We know this from Coulomb's law The direction will also be different

Electric Field Lines The electric field will show up as arrows drawn at various points around charged objects. These electric field lines (or electric force lines)are drawn below for two simple examples: a negative and positive source charge.

Constant Uniform Electric Field Lines Constant, uniform electric field lines can be created with parallel plates of different charges There’s slight curvature at the end, but this is often ignored since it is ofen small compared to the length of the plate

Force on a charge in an electric field If a charged particle q is placed in a region where there is an electric field is E: – The direction of F is the same as the direction of E if q is positive. – The direction of F is opposite to the direction of E if q is negative.

Electric Field Inside Conductor The electric field is zero at all points inside a conductor in electrostatic equilibrium.

The electric field right at the surface of a charged conductor is perpendicular to the surface.

At the top the charge has maximum electrical potential energy If you release the charge it will accelerate downward While it falls electrical potential energy -> kinetic energy When it reaches the negative plate (reference point) it has no electrical potential energy, it’s all kinetic

Voltage –Relation to Electrical Potential Energy Voltage is the change in electric potential energy per unit charge Many names: electric potential difference, electric potential, potential difference (and voltage)

Voltage The potential difference from one point, A, to another point, B, is the work done against electrical forces in carrying a unit positive test charge from A to B. Represent potential difference by V=V B -V A – Units: Volts = joules/coulomb (work per charge) The work done in transporting charge q from A to B is – W = q(V B -V A )=qV

The electric potential V at a point in space is the sum of the potentials due to each charge because it is a scalar The electric potential, like the electric field, obeys the principle of superposition

Electron Volts Define one electron volt as the energy needed to move one electron through one volt of potential difference If you need to do a calculation of energy in electron volts, you just figure out how many elementary charges you have multiplied by the voltage they moved through.

What is the conventional current and why? Conventional current is the flow of positive charges flowing from the positive to the negative terminal. Historically, positive charges were identified as the ones that flowed in the circuit.

Ohm’s Law Raising resistance reduces current. Raising voltage increases current. We call this relationship Ohm’s Law

Electrical Power Power is defined as And so work is qV So P = qV/t And So

What affects the resistance of a conducting wire? Decreasing the length of a wire (L) or increasing the cross- sectional area (A) would increase conductivity. Also, the measure of a conductor's resistance to conduct is called its resistivity. Each material has a different resistivity.

Series Circuit Lab Summary The current passing through all parts of a series circuit is the same. I total = I 1 = I 2 = I 3 The sum of the voltage drops across each of the resistors in a series circuit equals the voltage of the battery. V total = V 1 + V 2 + V 3 +… Show, using these facts and Ohm’s Law, what the equivalent resistance is

Series Circuits Lab Summary

Parallel Circuits Lab Summary The sum of the currents through each of the resistors in a parallel circuit equals the current of the battery. I total = I 1 + I 2 + I 3 … The voltage across all the resistors in a parallel circuit is the same. V total = V 1 = V 2 = V 3 … Show, using these facts and Ohm’s Law, what the equivalent resistance is.

Parallel Circuits Lab Summary

Kirchhoff's Rules Kirchhoff's First rule, or junction rule is based on the law of conservation of charge. It states: At any junction point, the sum of all currents entering the junction point must equal the sum of all the currents exiting the junction. For example I 3 = I 1 + I 2

Kirchhoff's Rules Kirchhoff's Second rule, or loop rule is based on the law of conservation of energy. It states: The sum of all changes in potential around any closed path must equal zero. For example V = V 1 + V 2

EMF A battery is a source of voltage AND a resistor. Electromotive force (EMF) is the process that carries charge from low to high voltage. Another way to think about it is that EMF is the voltage you measure when no resistance is connected to the circuit. The terminal voltage (at the terminals of the battery when current flows is found : V T =E-Ir

Capacitance Capacitance reflects the ability of a capacitor to store charge In the picture below, the capacitor is symbolized by a set of parallel lines. Once it's charged, the capacitor has the same voltage as the battery (1.5 volts on the battery means 1.5 volts on the capacitor )

Measuring Capacitance Let’s go back to thinking about plates! The unit for capacitance is the FARAD, F.

Capacitor Geometry The capacitance of a capacitor depends on HOW you make it. It is a geometric property

Capacitance When a battery is connected to a capacitor, charge moves between them. Every electron that moves to the negative plate leaves a positive nucleus behind. As the plates charge, the potential difference between the places increases. The current through the circuit decreases until the capacitor becomes fully charged.

Equivalent Capacitance –Parallel Circuits The voltage across each capacitor is the same. V = V 1 = V 2 The total charge is the sum of the charge on all the capacitors. Q = Q 1 + Q 2

Equivalent Capacitance –Parallel Circuits

Equivalent Capacitance –Series Circuits The sum of the voltage drops across each of the resistors in a series circuit equals the voltage of the battery. V = V 1 + V 2 The charge on each capacitor is the same. Q = Q 1 = Q 2

Equivalent Capacitance –Series Circuits

Magnetic Fields Magnetic fields can be visualized using magnetic field lines, which are always closed loops. Magnetic fields are always drawn coming out of the north pole and going into the south pole. The more lines per unit area, the stronger the field.

“B”“B” The magnetic field is often expressed as B. The field is a vector and has both magnitude and direction. UNITS The SI unit of B is the tesla, T. The gauss, G, is common as well 1 G =10 -4 T To gain perspective, the weak magnetic field of the Earth at its surface is around 0.5 x 10-4 T or simply 0.5 G.

Current-Carrying Wire A current-carrying wire produces a magnetic field around the wire – Concentric circles in plane perpendicular to the wire represent the magnetic field graphically – Compass needles align tangent to arcs of the magnetic field lines circling a current-carrying wire, indicated direction of field – Get direction of field from right hand rule

The Right Hand Rule The direction of the field is given by a right-hand rule. First, orient your right hand thumb in the direction of the current... Then wrap your fingers in the direction of the B Field.

Magnetic Field: The 3 rd Direction Picture the field line like an arrow. The head of the arrow is the direction of the field. If the magnetic field is into the page, you will see the tail of the arrow. If the magnetic field is out of the page, you will see the front of the arrow.

Force on electric current in a magnetic field A magnet exerts a force on a current-carrying wire. The direction of the force is given by another different right-hand rule. The force on the wire depends on the current, the length of the wire, the magnetic field, and its orientation. This equation defines the magnetic field, B.

Right Hand Rule -Flat Orientate your thumb so it’s in the direction on the current Point your palm in the direction the force Your fingers point in the direction of the magnetic field

Force on Electric Charge Moving in Magnetic Field The magnitude of force of a magnetic field of strength B on a single moving charge q, is a function of the velocity of the particle v, and its angular orientation Force maximum when velocity and current are perpendicular and 0 N when they are parallel

Right Hand Rule -Flat Orientate your thumb so it’s in the direction of the velocity (and current!) Point your palm in the direction the force Your fingers point in the direction of the magnetic field

For a negative charge just put the force in the opposite direction

Force on an Electric Charge Moving in a Magnetic Field If a charged particle is moving perpendicular to a uniform magnetic field, its path will be a circle.

Magnetic Field Due to a Straight Wire The strength of magnetic field due to a long straight wire is proportional to the current in the wire I, and inversely proportional to the distance from the wire r Where the permeability of free space is

Force Between Two Current Carrying Wires Two current carrying wires will interact with each other.

Visualization Parallel currents in the same direction attract

Visualization Parallel currents in the opposite direction repel X

Concept Check: Right Hand Rule What is the direction of the force on the current carrying wire (green) in the magnetic field (red)?

Concept Check Which diagram correctly shows the magnetic field inside and outside a current carrying loop of wire?

Concept Check: Right Hand Rule What is the direction of the force on the current carrying wire (green) in the magnetic field (red)?

Concept Check: Right Hand Rule What is the direction of the force on the current carrying wire (green) in the magnetic field (red)?

Concept Check Which diagram correctly shows the magnetic field around a current carrying wire?

Concept Check What is the direction of the force on the proton shown below?

Faraday’s Law Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil. Changes could come from anything – Changing magnetic field strength – Moving magnet w.r.t. the coil – Moving the coil w.r.t. a magnetic field – Rotating the coil relative to the magnetic field

Faraday’s Law – where N = number of turns (always 1 on AP B) – Φ = BA = magnetic flux – B = the external magnetic field – A = area of the coil On the equation sheet

Magnetic Flux Magnetic flux is the product of the average magnetic field times the perpendicular area that it penetrates. The area must be perpendicular to the magnetic field. SI Unit = Weber (Wb) or Volt/s Since we model a magnetic field with field line, you can think of flux as the number of field lines passing through a given area

Lenz’s Law When an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it.

Lenz’s Law

Lenz’s Law Practice The conducting rectangular loop falls through the magnetic field shown. What direction is the conventional current induced in the loop as it leave the field?

Lenz’s Law Practice A circular wire loop sits inside a larger circular loop that is connected to a battery as shown. Determine the direction of the convention current induced in the inner loop when the switch in the outer circuit is closed.

Lenz’s Law Practice A circular wire loop sits below a falling magnet as shown. Determine the direction of the conventional current induced in the loop as the magnet approaches the loop.