Q1a. Deriving the Electric Potential of a Dipole at a Distant Point

Background

Topic: Electrostatics – Electric Potential of a Dipole

This question tests your understanding of how to derive the electric potential at a point along the axis of a dipole, starting from the potential due to a single point charge.

Key Terms and Formulas:

• Electric potential due to a point charge:

• Dipole: Two equal and opposite charges separated by distance

• For large (far from dipole):

Step-by-Step Guidance

1. Write the expression for the potential at point due to each charge: and .

2. Add the potentials to get the total potential at : .

3. Combine the fractions and simplify the numerator and denominator.

4. For , use a binomial approximation to simplify the expression further.

Try solving on your own before revealing the answer!

Q1a ii. Electron Released Near a Dipole: Calculating Speed

Background

Topic: Energy Conservation in Electrostatics

This question tests your ability to use the change in electric potential energy to find the speed of an electron moving in the field of a dipole.

Key Terms and Formulas:

• Potential energy change:

• Conservation of energy:

• Electron charge: C

• Electron mass: kg

Step-by-Step Guidance

1. Calculate the potential at m and m using the dipole formula from part i.

2. Find the change in potential .

3. Calculate the change in potential energy: (since the electron has charge ).

4. Set equal to the kinetic energy and solve for .

Try solving on your own before revealing the answer!

Q1b. Calculating Currents in a Multi-Loop Circuit

Background

Topic: DC Circuits – Kirchhoff's Laws

This question tests your ability to analyze a circuit with multiple loops and resistors using Kirchhoff's rules.

Key Terms and Formulas:

• Kirchhoff's Current Law (KCL): at a junction

• Kirchhoff's Voltage Law (KVL): around a loop

• Ohm's Law:

Step-by-Step Guidance

1. Label the currents in each branch (e.g., through 3 Ω and 1 Ω, through 9 Ω and 18 Ω).

2. Write KVL equations for each loop, including the voltage sources and resistors.

3. Write KCL equations at the junctions to relate the currents.

4. Set up the system of equations and solve for the currents in each resistor.

Try solving on your own before revealing the answer!

Q3a. Fraction of Light Intensity Through Three Polarizers

Background

Topic: Polarization of Light

This question tests your understanding of how light intensity changes as it passes through multiple polarizers at different angles.

Key Terms and Formulas:

• Malus's Law:

• For unpolarized light, first polarizer:

• Subsequent polarizers:

Step-by-Step Guidance

1. Calculate the intensity after Polarizer 1: .

2. Calculate the intensity after Polarizer 2: .

3. Calculate the intensity after Polarizer 3: .

4. Multiply the fractions to find the total fraction of emerging from the system.

Try solving on your own before revealing the answer!