Q1. Calculate the electric field at point p due to the two charges, giving the result in component form.

Background

Topic: Electric Field from Point Charges

This question tests your ability to calculate the electric field at a specific point due to multiple point charges, using vector addition and component analysis.

Key Terms and Formulas:

• Electric field due to a point charge:

• Superposition principle: The total electric field is the vector sum of fields from each charge.

• Key constants:

• Component form:

Step-by-Step Guidance

1. Identify the positions of the charges and point p. The charges are at (0, +2 cm) and (0, -2 cm), and point p is at (-4 cm, 0).

2. Calculate the distance from each charge to point p using the Pythagorean theorem: .

3. Determine the direction of the electric field produced by each charge at point p. Since both charges are positive, the field points away from each charge.

4. Calculate the electric field magnitude from each charge at point p using , then resolve each field into x and y components.

5. Add the x and y components from both charges to find the total electric field at point p in vector form.

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Q2. Does the pyramid-shaped object contain positive, negative, or zero charge? Explain using electric flux.

Background

Topic: Gauss' Law and Electric Flux

This question tests your understanding of Gauss' Law, which relates the net electric flux through a closed surface to the net charge enclosed by that surface.

Key Terms and Formulas:

• Electric flux:

• Gauss' Law:

• Net flux: Sum the flux through all faces to determine the net charge inside.

Step-by-Step Guidance

1. Calculate the electric flux through each face: for each face.

2. Sum the fluxes from all five faces to find the total net flux through the pyramid.

3. Apply Gauss' Law: If the net flux is positive, the object contains positive charge; if negative, negative charge; if zero, no net charge.

4. Check the direction of each electric field relative to the surface normal to determine the sign of each flux.

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Q6. If wire A has a diameter of 0.8 cm and electron drift speed of m/s, what is the electron drift speed in wire B (diameter 1.6 cm), given the same current?

Background

Topic: Microscopic View of Current

This question tests your understanding of how drift speed relates to current, cross-sectional area, and charge carrier density in wires.

Key Terms and Formulas:

• Current:

• = number density of electrons, = elementary charge, = cross-sectional area, = drift speed

• For same current and material, and are constant.

Step-by-Step Guidance

1. Write the current equation for both wires:

2. Express the cross-sectional area: ; calculate and using the diameters.

3. Set up the ratio: , then solve for in terms of and the areas.

4. Plug in the values for diameters and drift speed to find .

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Q7. Plot a graph of voltage as a function of location in the circuit, tracing the loop clockwise from point A.

Background

Topic: Kirchhoff's Junction Rule and Voltage Drops

This question tests your ability to analyze voltage changes in a circuit as you move through batteries and resistors, using Kirchhoff's rules.

Key Terms and Formulas:

• Kirchhoff's Loop Rule: The sum of voltage changes around a closed loop is zero.

• Voltage drop across resistor:

• Voltage rise across battery:

Step-by-Step Guidance

1. Start at point A and note the initial voltage.

2. Move through the 12 V battery (voltage rises), then through the 3 Ω resistor (voltage drops by ).

3. Continue through the 6 V battery (voltage rises), then through the 2 Ω resistor (voltage drops by ).

4. Plot the voltage at each segment, showing rises and drops as you trace the loop.

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