Q1. What acceleration will a +20 pC charge with a mass of 2 µg experience if it moves perpendicular to a magnetic field of 0.080 T at a speed of 4.8 cm/s?

Background

Topic: Magnetic Force on a Moving Charge

This question tests your understanding of the force experienced by a charged particle moving in a magnetic field and how to relate that force to acceleration using Newton's second law.

Key Terms and Formulas

• Magnetic force on a moving charge: (when velocity is perpendicular to the field)

• Acceleration:

• Where:

  • = charge (in coulombs)

  • = speed (in m/s)

  • = magnetic field strength (in tesla)

  • = mass (in kg)

Step-by-Step Guidance

1. Convert all quantities to SI units: , , , .

2. Calculate the magnetic force using .

3. Use Newton's second law to relate force to acceleration: .

4. Set up the expression for acceleration: .

Try solving on your own before revealing the answer!

Q2. An experimental magnetic field of 1000 T was briefly created in 1967. Suppose a wire 25 cm long was placed in this magnetic field perpendicular to the field and experienced a force of 160 N. What current was moving in the wire at the time?

Background

Topic: Magnetic Force on a Current-Carrying Wire

This question tests your ability to use the formula for the force on a wire carrying current in a magnetic field.

Key Terms and Formulas

• Magnetic force on a wire: (when wire is perpendicular to the field)

• Where:

  • = force (in newtons)

  • = current (in amperes)

  • = length of wire (in meters)

  • = magnetic field strength (in tesla)

Step-by-Step Guidance

1. Convert the length to meters: .

2. Write the formula for force: .

3. Rearrange to solve for current: .

4. Plug in the values: , , .

Try solving on your own before revealing the answer!

Q3. What is the magnitude and magnetic field 20 cm above a wire carrying 4 A of current from right to left?

Background

Topic: Magnetic Field Due to a Long Straight Current-Carrying Wire

This question tests your ability to use the formula for the magnetic field at a distance from a straight wire.

Key Terms and Formulas

• Magnetic field at distance from a wire:

• Where:

  • = permeability of free space ()

  • = current (in amperes)

  • = distance from wire (in meters)

Step-by-Step Guidance

1. Convert the distance to meters: .

2. Write the formula for the magnetic field: .

3. Plug in the values: , , .

4. Set up the calculation for .

Try solving on your own before revealing the answer!

Q4. Two wires, each having a weight of 1.0 x 10-4 N per meter are strung parallel to each other above the surface of the Earth, one directly above the other. The wires are aligned north-south so Earth’s magnetic field will not affect them. When their distance of separation is 0.10 m, what must be the current in each (assumed to be the same magnitude but in opposite directions) in order for the lower wire to levitate the upper wire?

Background

Topic: Magnetic Force Between Parallel Wires

This question tests your understanding of the force between two parallel wires carrying current and how it can balance the weight of one wire.

Key Terms and Formulas

• Magnetic force per unit length between two wires:

• Where:

  • = permeability of free space ()

  • = currents in the wires (in amperes)

  • = distance between wires (in meters)

Step-by-Step Guidance

1. Set the magnetic force per unit length equal to the weight per unit length: .

2. Write the formula for the force per unit length: (since ).

3. Rearrange to solve for : .

4. Plug in the values: , , .

Try solving on your own before revealing the answer!

Q5. A unicycle wheel has 200 turns of thin wire wrapped around its rim. The wheel itself has a diameter of 2.5 cm. What emf is induced in the wire when the wheel is perpendicular to a magnetic field that steadily decreases from 0.68 T to 0.24 T in 4.5 s? What current is induced in wire if it has a resistance of 6.8 mΩ?

Background

Topic: Electromagnetic Induction (Faraday's Law)

This question tests your ability to use Faraday's law to calculate induced emf and Ohm's law to find the induced current.

Key Terms and Formulas

• Faraday's law:

• Magnetic flux:

• Ohm's law:

• Where:

  • = number of turns

  • = change in magnetic flux

  • = time interval

  • = magnetic field

  • = area of loop

  • = resistance

Step-by-Step Guidance

1. Calculate the area of the wheel: , where .

2. Find the change in magnetic flux: .

3. Use Faraday's law to find the induced emf: .

4. Use Ohm's law to find the induced current: , with .

Try solving on your own before revealing the answer!

Q6. What is the time constant for an LR circuit with a resistance of 160 Ω and a 35 mH inductor? How long will it take for the circuit to reach 80% of its maximum current once the switch is closed?

Background

Topic: LR Circuits (Inductive Time Constant)

This question tests your understanding of the time constant in an LR circuit and how to use it to determine the time to reach a certain percentage of maximum current.

Key Terms and Formulas

• Time constant for LR circuit:

• Current as a function of time:

• Where:

  • = inductance (in henries)

  • = resistance (in ohms)

  • = time constant (in seconds)

  • = maximum current

Step-by-Step Guidance

1. Convert inductance to henries: .

2. Calculate the time constant: .

3. Set up the equation for current: .

4. Set and solve for .

Try solving on your own before revealing the answer!

Q7. An LRC circuit is comprised of a 25 Ω resistor, a 15 mH inductor, and a 60 µF capacitor all connected in series with a 120 V 250 Hz AC power source. Determine the power through the inductor.

Background

Topic: AC Circuits (LRC Series Circuit)

This question tests your ability to analyze power in an AC circuit, specifically through the inductor.

Key Terms and Formulas

• Inductive reactance:

• Impedance:

• Current:

• Power through inductor:

• Where:

  • = frequency (in Hz)

  • = inductance (in henries)

  • = capacitance (in farads)

  • = voltage (in volts)

Step-by-Step Guidance

1. Convert inductance and capacitance to SI units: , .

2. Calculate inductive reactance: .

3. Calculate capacitive reactance: .

4. Calculate impedance: .

5. Set up the formula for power through the inductor: , where .

Try solving on your own before revealing the answer!

Q8. A beam of light, traveling in air, strikes the surface of mineral oil at an angle of 23.1º with the normal to the surface. If the light travels at 2.17 x 108 m/s through the oil, what is the angle of refraction?

Background

Topic: Refraction (Snell's Law)

This question tests your ability to use Snell's law to find the angle of refraction when light passes from one medium to another.

Key Terms and Formulas

• Snell's law:

• Index of refraction:

• Where:

  • = index of refraction of air (approximately 1)

  • = index of refraction of oil

  • = angle of incidence

  • = angle of refraction

  • = speed of light in vacuum ()

  • = speed of light in oil

Step-by-Step Guidance

1. Calculate the index of refraction for mineral oil: , where .

2. Set up Snell's law: .

3. Plug in , , and from step 1.

4. Rearrange to solve for : .

Try solving on your own before revealing the answer!

Q9. A plastic pipe has an index of refraction of 1.53. For total internal reflection, what is the minimum angle of incidence to the wall of the pipe if the pipe is in water?

Background

Topic: Total Internal Reflection

This question tests your understanding of the conditions for total internal reflection and how to calculate the critical angle.

Key Terms and Formulas

• Critical angle:

• Where:

  • = index of refraction of plastic pipe

  • = index of refraction of water (typically about 1.33)

Step-by-Step Guidance

1. Identify (plastic pipe), (water).

2. Set up the formula for the critical angle: .

3. Plug in the values for and .

Try solving on your own before revealing the answer!

Q10. A spherical Christmas ornament is 6.00 cm in diameter. What is the magnification of an object placed 10.0 cm away from the ornament? Is the image upright or inverted?

Background

Topic: Spherical Mirrors (Magnification)

This question tests your ability to use the mirror equation and magnification formula for spherical mirrors.

Key Terms and Formulas

• Mirror equation:

• Magnification:

• Where:

  • = focal length (for a sphere, )

  • = object distance

  • = image distance

Step-by-Step Guidance

1. Calculate the radius of the ornament: .

2. Find the focal length: .

3. Use the mirror equation to solve for .

4. Set up the magnification formula: .

Try solving on your own before revealing the answer!

Q11. A convex lens of focal length 15.0 cm is used as a magnifying glass. At what distance from a postage stamp should you hold this lens to get a magnification of +2.00?

Background

Topic: Lenses (Magnification and Lens Equation)

This question tests your ability to use the lens equation and magnification formula for a convex lens.

Key Terms and Formulas

• Lens equation:

• Magnification:

• Where:

  • = focal length

  • = object distance

  • = image distance

Step-by-Step Guidance

1. Set up the magnification formula: , with .

2. Express in terms of : .

3. Use the lens equation: .

4. Substitute into the lens equation and solve for .

Try solving on your own before revealing the answer!

Q12. Two converging lenses are placed 20 cm apart. The first lens has a focal length of 10.0 cm and the second has a focal length of 20.0 cm. Locate the final image formed of an object 30.0 cm in front of the first lens. Determine the magnification of the system. Is the final image upright or inverted?

Background

Topic: Multiple Lens Systems

This question tests your ability to analyze a system with two lenses, including image location and magnification.

Key Terms and Formulas

• Lens equation:

• Magnification for each lens:

• Total magnification:

• Where:

  • = focal length

  • = object distance

  • = image distance

Step-by-Step Guidance

1. Use the lens equation for the first lens to find the image distance .

2. Calculate the object distance for the second lens: (taking sign conventions into account).

3. Use the lens equation for the second lens to find the final image distance .

4. Calculate the magnification for each lens and multiply to find the total magnification.

Try solving on your own before revealing the answer!