PHYSICS 222 SI FINAL EXAM REVIEWWITH SI LEADER: ROSALIE

ELECTROSTATICS THEORY

• Two point charges, +q and (unknown) Q produce the net electric field shown at point p in the figure. What is the charge Q in terms of q?

SOLUTION

• Q = -q

If the magnitude of Q were any greater or less than q, the vector E would have some force in the x direction. It doesn’t, so we know the magnitude of Q must be the same as q. We also know that the charge of Q must be opposite, to push the particle the same way that q pulls it.

ELECTROSTATICS THEORY

• Two uncharged metal spheres are touching. A third, positively charged sphere is placed to the left of sphere 1. With this third sphere still in place, spheres 1 and 2 are moved away from each other so that they are no longer touching, and the third sphere is removed. What are the charges on spheres 1 and 2?

3

1 2

SOLUTION

• Sphere 1 is negatively charged and sphere 2 is positively charged. (Try to draw a diagram, it helps!)

CONDUCTORS

• An uncharged conducto has a hollow cavity inside of it. Within this cavity, there is a charge of +10 C that does not touch the conductor. There are no other charges in the vicinity. What are the charges of the inner and outer surfaces of the conductor?

SOLUTION

• The charge on the inner surface is -10 C and the charge on the outer surface is 10 C (A diagram helps on this one as well)

ELECTROSTATICS - THEORY

• The figure shows three chargers labeled , and electric field lines in the region surrounding the charges. What are the signs of these charges?

SOLUTION

• is positive• is negative• Electric field lines start at positive charges and end at

negative charges.

ELECTROSTATICS -1

• A solid metal ball of radius 2.0 cm carries a total charge of -0.1 μC. What is the magnitude of the electric field at a distance from the ball center of 1.0cm?

ELECTROSTATICS – 1 SOLUTION

• 0

• Conductors carry charge on their surface. A charge inside of a conductor is 0.

ELECTROSTATICS

When two point charges are a distance d part, the electric force that each one feels from the other has magnitude F. In order to make this force twice as strong, what would the distance have to be changed to?

ELECTROSTATICS SOLUTION

If , then in order to make one half of its original value, it is necessary to divide d by

FLUX AND GAUSS LAW

• A point charge is located on the x-axis at x = 2.1 m, and a second point charge is on the y- axis at y = 1.15 m. What is the total electric flux due to these two point charges through a spherical surface centered at the origin with radius r = 1.55 m?

SOLUTION

• Charge 1 isn’t enclosed in the sphere, but charge 2 is. The equation for flux is:

MAGNETIC FIELDS

• A small metal rod has a mass of 0.1 kg and it lies in a magnetic field of 1 T. If the rod is 1 m long and carries a current, what current is necessary so that the net force on the rod is zero?

SOLUTION

• F = mg = IL x B I x (1m X 1T) = .1kg x 9.8 m/s^2 solve for I = 98 A

MAGNETIC FIELD

• A 1 m by 1 m circuit containing only a 50 Ω resistor lies perpendicular in a magnetic field. The magnetic field changes from 5 T to 1 T in 30 ms. What is the magnitude of the induced current?

SOLUTION

• Induced emf is ε = -dΦ/dt = -AdB/dt = (1m2)(4T) / (30 ms) = 133.33 V which is equal to IR so current is 2.66 A

FLUX AND GAUSS LAW

• What is the net flux through a cube of side 10 cm if a + 2 C point charge is placed 20 cm from the center of the cube?

SOLUTION

• 0

There is no charge inside of the cube, so there is no flux.

MAGNETIC FIELD

• An electron moving with a velocity = 5.0 × m/s enters a region of space where perpendicular electric and magnetic fields are present. The electric field is E = 1j. What magnetic field will allow the electron to go through the region without being deflected?

SOLUTION

• If the electron is to keep the same velocity and path, the force from the magnetic field must be the same as the force from the electric field so:

F = qE = qv x B

-1.6 x N j = 8 x i x B

-1.6 x N j = (0 – 0)i + (0 – (8 x )())j + ((8 x ) – 0)k

-1.6 x N j = - (8 x )()j

B = 2 x T k

CIRCUITRY -1 Consider a fully-charged parallel plate capacitor. The capacitor is far from other objects and is not connected to a battery. The plates are now being pulled apart. What happens to the potential difference between the plates as they are being separated?

a) It decreases

b) It increases

c) It remains constant

d) It is zero

e) Cannot be determined from given information

CIRCUITRY 1 – SOLUTION

• B) It increases!

• ∆V = Ed

Where d is the distance apart. As d increases, so does ∆V!

CIRCUITRY 2

Two resistors of 15 and 30 Ω are connected in parallel. If the combination is connected in series with a 9.0-V battery and a 20-Ω resistor, what is the current through the 15-Ω resistor?

CIRCUITRY 2 - SOLUTION

• I = .2 A

9v

20 Ω

30 Ω

15 Ω

Use the loop rule (the sum of potential drops around any loop is 0) around the left loop and the outer loop

Use the junction rule (the sum of all currents entering a junction must be the same as he sum of all current exiting the junction) on the upper junction

+

Solve these as a system of equations for , then use to find = .2 A

LR CIRCUIT

• A series LR circuit consists of a 2.0-H inductor with negligible internal resistance, a 100-ohm resistor, an open switch, and a 9.0-V ideal power source. After the switch is closed, what is the maximum power delivered by the power supply?

SOLUTION

Since the question asks about the maximum power, the current will be maximal (and constant) and the inductor will just act like a piece of wire.

LRC CIRCUIT

In a series LRC circuit, the frequency at which the circuit is at resonance is . If you double the resistance, the inductance, the capacitance, and the voltage amplitude of the ac source, what is the new resonance frequency?

SOLUTION

• The circuit is at resonance when =

POWER

• If you have 2 circuits each connected to a 120 V power source and each containing 3 bulbs of resistance 20 Ω (one circuit has the three bulbs in parallel and the other has the bulbs in series), which bulbs will glow the brightest? What is the power delivered to each bulb?

SOLUTION

First, solve for the current going through each bulb in the top circuit (Kirchoff’s laws are handy for this):

120V = (I)(20Ω) I = 6 A

Plug this into out power equation: = 2400 W

Now find the power in the second loop: find the current through the circuit:

V = IR 120 = (I)(60) I = 2 A

= 800 W

So: > and the series bulbs glow the brightest!

120

V

120

V

AC CIRCUITS

• Which one of the phasor diagrams shown below best represents a series LRC circuit driven at resonance?

AC CIRCUIT SOLUTION

• At resonance, so it must be #3

ELECTROMAGNETIC WAVES

• An electromagnetic wave with frequency 64 Hz travels in an insulating magnetic material that has dielectric constant 3.64 and relative permeability 5.18. At this frequency, the electric field has amplitude 7.2 V/m. Determine the speed of propagation of the wave, the wavelength, and the amplitude of the magnetic field.

SOLUTION

LIGHT WAVES

• A laser emits 1.00 mW of average light power in a cylindrical beam of radius 5.00 mm. The intensity of the light at a point in the beam is ____ W/m2

SOLUTION

•

• = 12.7

POLARIZATION

A beam of unpolarized light of intensity I0 passes through a series of ideal polarizing filters with their polarizing directions turned to various angles as shown in the figure. What are the intensities at points a and b?

SOLUTION

• and natural light going through a single filter is reduced to one half its original value

LAB QUESTION

• In experiment RR – Reflection and refraction, you used the set up shown in the figure below. A monochromatic laser beam is incident onto the flat side of a semi-circular prism, right at its center. The orientation angles of the flat side of the prism (α) and of the refracted ray (β) are measured relative to the direction of the incident ray. For the first orientation you try, α = 37° and β = 155°. For a good measurement of the index of refraction, we will have to get many more measurements, but we can use the first one to obtain a rough estimate. Based on this first measurement, what is the index of refraction of the material?

SOLUTION

• Snells law:

• Since the medium for this system is air, = 1.

• θ1

θ2

Angles 1 and 2 are the angles between the incoming and refracted ray and the normal to the surfaceSo: + α = 90° = 53° + α + 90° = β = 28°

(1)28= 1.7

MIRROR

A dentist uses a curved mirror to view teeth on the upper side of the mouth. Suppose she wants an erect image with a magnification of 2.00 when the mirror is 1.25 cm from a tooth. (Treat this problem as though the object and image lie along a straight line.) Determine what kind of mirror is needed using a ray diagram, and determine the focal length and radius of curvature of the mirror

SOLUTION

• 2

LENSES

• Draw a lens diagram for the following lenses and define the images:

Converging lens Diverging lens

LENSES SOLUTION

• Draw a lens diagram for the following lenses and define the images:

Real, inverted, diminished Imaginary, upright, diminished

SIGN CONVENTIONS FOR LENSES

• Object distance (s) is positive if it is on the same side as incoming light – otherwise negative (the left side)

• Image distance (s’) is positive if on the same side as outgoing light – otherwise negative (the right side)

• Radius of curvature (R) is positive if the center of curvature is on the same side as outgoing light, otherwise negative. (the center of the circle is on the right side)

LENS PROBLEM

Consider an object with s = 12 cm that produces an image with s’ = 15 cm.

• Find the focal length

• Tell whether the image is real or virtual

SOLUTION

• f = 6.67 cm

• The image is real because s’ is positive

LENS

A converging lens has a focal length f. An object is placed at a distance between f and 2f on a line perpendicular to the center of the lens. The image formed is located at what distance from the lens?

• A) between the lens and f

• f

• 2f

• Farther than 2f

• Between f and 2f

SOLUTION

• Larger than 2f

• Draw a lens diagram

LENSES

• A glass converging lens has one flat side and one side with a radius of curvature of 20.0 cm. The focal length of the lens is ____ cm. (The index of refraction of the glass in the lens is 1.50)

SOLUTION

•

• f = 40 cm

2 SLIT

• In a double slit experiment, if the slit separation is increased, which of the following happens to the interference pattern?

SOLUTION

• Minima locations are given by so if d increases, y decreases meaning that the minima get closer together.

RELATIVITY

• A man stands in the exact center of a glass freight car moving at very high speed. He holds a flashlight in each hand and directs them at opposite walls, switching them on at the same time. You stand still outside of the freight train and watch it go by. In the mans frame of reference, which beam of light travels faster? In your frame of reference which beam of light travels faster? In the mans frame of reference which wall is struck by light first? In your fram of reference which wall is struck by light first?

SOLUTION

• Light always moves at the same speed, c, no matter what the frame of reference is. So we see the light moving at the same speed as the man does.

• The man sees the light hitting both walls at the same time. However, we see the light hit the rear wall first, because the rear wall moves “towards” the beam of light, while the front wall moves “away” from the light. Isn’t relativity fun?

RELATIVITY

• A star is moving towards the earth with a speed at 90% of the speed of light. It emits light, which moves away from the star in every direction at the speed of light, c. Relative to us on earth, what is the speed of light moving toward us from the star?

SOLUTION

• C. Light always moves at the speed of light, no matter what the reference frame is.

HEISENBERG UNCERTAINTY

• If the accuracy in measuring the position of a particle increases, the accuracy in measuring its velocity will do what?

• A) increase

• B) remain the same

• C) decrease

• D) it is impossible to say since the two measurements are unrelated and do not affect each other

SOLUTION

• It decreases

Heisenberg’s uncertainty principle tells us that

This means that if the accuracy in x increases, the opposite must be true of p.

QUESTIONS?