Q1. What is the maximum velocity () of an alpha particle () in an electric field with a potential difference of 100 V?

Background

Topic: Energy conservation in electric fields

This question tests your understanding of how a charged particle (here, an alpha particle) gains kinetic energy when accelerated through a potential difference. The work done by the electric field on the particle is converted into kinetic energy.

Key Terms and Formulas

• Alpha particle (): Helium nucleus, charge , mass kg

• Potential difference (): The voltage the particle moves through

• Energy conservation:

Step-by-Step Guidance

1. Identify the charge of the alpha particle: C.

2. Write the energy conservation equation: .

3. Rearrange the equation to solve for : .

4. Plug in the known values for , , and (but do not calculate the final value yet).

Try solving on your own before revealing the answer!

Q2. If an alpha particle moves from point A to point B between equipotential lines (A at 10 V, B at 30 V), how much energy is required?

Background

Topic: Work done by electric field and potential difference

This question tests your understanding of how the work required to move a charge between two points in an electric field depends on the potential difference and the charge.

Key Terms and Formulas

• Work done ():

• Alpha particle:

Step-by-Step Guidance

1. Determine the charge of the alpha particle: .

2. Calculate the potential difference: .

3. Use the formula to set up the calculation.

4. Substitute the values for and (but do not compute the final value yet).

Try solving on your own before revealing the answer!

Q3. If a 7.0 μC charge is allowed to move from B to A (B at 30 V, A at 10 V), and the charge mass is 2 mg, what is (final velocity)?

Background

Topic: Conservation of energy in electric fields

This question tests your ability to relate the change in electric potential energy to the kinetic energy gained by a charge moving between two points of different potential.

Key Terms and Formulas

• Potential energy change:

• Kinetic energy:

• Conservation:

Step-by-Step Guidance

1. Identify the charge ( C) and mass ( kg).

2. Calculate the potential difference: .

3. Set up the energy equation: .

4. Rearrange to solve for : .

5. Substitute the known values, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q4. A ion is accelerated through a 0.150 MV potential difference and reaches a final velocity of m/s. What is its mass?

Background

Topic: Energy conservation for ions in electric fields

This question tests your ability to use the relationship between electric potential energy and kinetic energy to solve for the mass of an ion.

Key Terms and Formulas

• Charge of :

• Potential difference: V

• Final velocity: m/s

• Energy conservation:

Step-by-Step Guidance

1. Identify the charge: C.

2. Write the energy equation: .

3. Rearrange to solve for : .

4. Substitute the known values for , , and (but do not calculate the final value yet).

Try solving on your own before revealing the answer!

Q5. A negatively charged particle is suspended between two plates 20 cm apart with a voltage of V. The electric force is N. What are the charge () and mass () of the particle?

Background

Topic: Forces on charges in electric fields and equilibrium

This question tests your understanding of the relationship between electric force, electric field, and the equilibrium of a charged particle in a uniform electric field.

Key Terms and Formulas

• Electric field:

• Electric force:

• Equilibrium: (if the particle is suspended and not accelerating)

Step-by-Step Guidance

1. Calculate the electric field: , where V and m.

2. Use to solve for the charge .

3. If the particle is in equilibrium, set to solve for the mass .

4. Substitute the known values, but do not compute the final values yet.

Try solving on your own before revealing the answer!