Physics 114 First Midterm

A large, metallic, spherical shell has no net charge. It is supported on an insulating stand and has a small hole at the top. A small tack with charge Q is lowered on a silk thread through the hole into the interior of the shell. (iii) The tack is now allowed to touch the interior surface of the shell. After this contact, what is the charge on the tack? Q Q/2 0 −Q/2 −Q

0

A large, metallic, spherical shell has no net charge. It is supported on an insulating stand and has a small hole at the top. A small tack with charge Q is lowered on a silk thread through the hole into the interior of the shell. (iv) What is the charge on the inner surface of the shell now after the tack touches it? Q Q/2 0 −Q/2 −Q

0

Resistivity and Temperature

Resistivity in metals is linear with temperature over a limited range

Electric dipole

two charges of equal magnitude but opposite sign

Energy Density

ue=0.5epsilonE^2

Three wires are made of copper having circular cross sections. Wire 1 has a length L and radius r. Wire 2 has a length L and radius 2r. Wire 3 has a length 2L and radius 3r. Which wire has the smallest resistance? wire 1 wire 2 wire 3 All three wires have the same resistance. Not enough information is given to answer the question.

wire 3

(i) What happens to the magnitude of the charge on each plate of a capacitor if the potential difference between the conductors is doubled? It becomes four times larger. It becomes two times larger. It is unchanged. It becomes one-half as large. It becomes one-fourth as large. (ii) If the potential difference across a capacitor is doubled, what happens to the energy stored? It becomes four times larger. It becomes two times larger. It is unchanged. It becomes one-half as large. It becomes one-fourth as large.

(i) It becomes two times larger. (ii)It becomes two times larger.

Electric Potential

(volts-v-J/C) it is a scalar quantity and can depend solely on electric field and distance

Calculating Capacitance

Assume a charge between plates --> calculate electric field using Gauss's law --> calculate the potential and then find the capacitance by q/v

Charged Conductor

Charge always resides at the outer surface The field lines are always perpendicular to surface The potential difference is zero on the surface Surface is equipotential Since E=0 inside the conductor, the V is constant and equal to the surface value

Van de Graff Generator

Charge is released inside sphere which goes to outer surface so process can be repeated over and over again

Resistor

Circuit elements with a well defined resistance

Total Charge in a System is

Conserved

Rank the Currents

Current in a branch is the same For the 60W bulb, the power is greater so the current is greater than for the 30w bulb THE TOTAL CURRENT IS CONSERVED

Non-Ohmic Devices

Diodes are devices that let current through one way much easier than the other way superconductors are cold materials that have no resistance at all

Electric Potential Energy

Displacement not distance traveled. Conservative force. positive charge moves in the direction of the electric field, its electric potential energy decreases

Equipotential Surfaces

Electric potential is CONSTANT and no work is done moving a particle across the surface

Conductors in Equilibrium

Electrons will accelerate in opposite directions of field lines, internal field opposing the external field is established and then they cancel each other out and then the Electric field is ZEROOOOO inside a conductor but the net charge will be on the surface

Cavity within a conductor

Field free E=zero everywhere inside the cavity

Conductors

Free movement of charges (metals)

Ohm's Law

In some materials, the field applied and the current density are proportional

Gauss's Law

It can be generalized to any surface. Net flux is determined by the charges INSIDE the surface. Electric field can be nonzero on the surface while net flux is zero.

A free electron and a free proton are released in identical electric fields. (ii) Compare the magnitudes of their accelerations. It is millions of times greater for the electron. It is thousands of times greater for the electron. They are equal. It is thousands of times smaller for the electron. It is millions of times smaller for the electron.

It is thousands of times greater for the electron.

Current Density

J=I/A= sigma*E NOT A MEASURED QUANTITY

Semi-conductors

Limited number of free carriers (silicon)

Current

Net flow rate of charges through a surface area (amperes=C/s) Direction of the positive charges. Negative charges will produce a current in the OPPOSITE direction

Electric Field

Newtons/Coulombs

Insulators

No movement of charges within the object (wood, plastic, rubber)

The Direction of A for Electric Flux

Perpendicular to the surface. For a closed surface, the surface normal points outward

A large, metallic, spherical shell has no net charge. It is supported on an insulating stand and has a small hole at the top. A small tack with charge Q is lowered on a silk thread through the hole into the interior of the shell. (ii) What is the charge on the outer surface of the shell? Q Q/2 0 −Q/2 −Q

Q

A large, metallic, spherical shell has no net charge. It is supported on an insulating stand and has a small hole at the top. A small tack with charge Q is lowered on a silk thread through the hole into the interior of the shell. (v) What is the charge on the outer surface of the shell now after the tack touches it? Q Q/2 0 −Q/2 −Q

Q

Conductors and Gauss's law

The Electric field just outside the conductor is perpendicular to the surface and is proportional to the charge density. The charge density is highest near parts of the conductor with the smallest radius of curvature.

Electric field lines

The electric field is tangent to the field lines, the density of the lines is proportional to the magnitude of the electric field, field lines cannot cross and go from positive to negative

Electrical Power

The energy supplied by a battery is converted to heat on the resistor. The rate of this conversion is the electrical power watts (J/s)

Choosing a Gaussian Surface

The field over the surface is constant in symmetry, the field and A vectors are parallel simplifying the dot product or they are perpendicular making it zero. OR the field is zero over the surface.

A free electron and a free proton are released in identical electric fields. (i) How do the magnitudes of the electric force exerted on the two particles compare? It is millions of times greater for the electron. It is thousands of times greater for the electron. They are equal. It is thousands of times smaller for the electron. It is millions of times smaller for the electron.

They are equal.

What happens when a charged insulator is placed near an uncharged metallic object? They repel each other. They may attract or repel each other, depending on whether the charge on the insulator is positive or negative. The charged insulator always spontaneously discharges. They attract each other. They exert no electrostatic force on each other.

They attract each other.

Energy stored in a capacitor

USE THE ONE THAT REMAINS CONSTANT!!!!! so if V remains constant then use 1/2cv^2

Dielectrics

Used to increase the charge storage capacity and/or the Max voltage in capacitors The dielectric constant is measure of the polarizability of the material (reduces effective voltage or if under a constant voltage allows a larger charge to collect)

A spherical surface surrounds a point charge q. Describe what happens to the total flux through the surface if the following happens: (a) The charge is tripled. The flux is tripled. The flux decreases by 1/3. The flux remains constant. The flux goes to zero . (b) The volume of the sphere is doubled. The flux is tripled. The flux decreases by 1/3. The flux remains constant. The flux goes to zero. (c) The surface is changed to a cube. The flux is tripled. The flux decreases by 1/3. The flux remains constant. The flux goes to zero. (d) The charged is moved to another location inside the surface. The flux is tripled. The flux decreases by 1/3. The flux remains constant. The flux goes to zero. (e) The charge is moved outside the surface. The flux is tripled. The flux decreases by 1/3. The flux remains constant. The flux goes to zero.

a) The flux is tripled. b)The flux remains constant. c)The flux remains constant. d) The flux remains constant. e) The flux goes to zero.

Induction

bring a charge near an extended conductor and charge moves in response and if you ground it the negative charge flows in

A metallic coin is given a positive electric charge. What happens to its mass? increase measurably increase by an amount too small to measure directly remain unchanged decrease by an amount too small to measure directly decrease measurably

decrease by an amount too small to measure directly

Important Capacitance Details

depends on STRUCTURE AND DIMENSIONS but NOT the voltage and charge (I.e if charge goes up, the voltage goes up to compensate for the change) One farad is VERY large

A fully charged parallel-plate capacitor remains connected to a battery while you slide a dielectric between the plates. Do the following quantities increase, decrease, or stay the same? (i) C increases decreases stays the same (ii) Q increases decreases stays the same (iii) ΔV increases decreases stays the same (iv) the energy stored in the capacitor increases decreases stays the same

i)increases ii)increases iii)stays the same iv)increases

Now the coin is given a negative electric charge. What happens to its mass? increase measurably increase by an amount too small to measure directly remain unchanged decrease by an amount too small to measure directly decrease measurably

increase by an amount too small to measure directly

Resistivity

inverse of conductivity Ohms

Electric Flux

proportional to the total number of electric field lines through a surface

A particle with charge q is located inside a cubical gaussian surface. No other charges are nearby. If the particle can be moved to any point within the cube, what maximum value can the flux through one face approach? 0 q/2ε0 q/6ε0 q/8ε0 depends on the size of the cube

q/2ε0

A particle with charge q is located inside a cubical gaussian surface. No other charges are nearby. (i) If the particle is at the center of the cube, what is the flux through each one of the faces of the cube? 0 q/2ε0 q/6ε0 q/8ε0 depends on the size of the cube

q/6ε0

Connected Charged Conducting Sphere

q1/q2=r1/r2 E1/E2=r2/r1

Capacitance

the ability of a conductor to store energy in the form of electrically separated charges Two conductors with equal but opposite charges which causes an electric field and that causes potential difference between the charge C/V= Farads (F)

A large, metallic, spherical shell has no net charge. It is supported on an insulating stand and has a small hole at the top. A small tack with charge Q is lowered on a silk thread through the hole into the interior of the shell. (i) What is the charge on the inner surface of the shell? Q Q/2 0 −Q/2 −Q

−Q