Q1. Two long straight wires are placed parallel to one another 9 cm apart. Wire 1 carries a current of 4 A out of the page, and wire 2 carries a current of 8 A into the page. A point P is located 6 cm to the right of wire 2. Calculate the magnitude of the magnetic field due to both wires at point P.

Background

Topic: Magnetic fields due to currents (Biot-Savart Law and Ampère’s Law)

This question tests your understanding of how to calculate the magnetic field produced by long, straight current-carrying wires at a specific point in space, and how to apply the superposition principle for vector fields.

Key Terms and Formulas

• Magnetic field due to a long straight wire:

• = permeability of free space ( T·m/A)

• = current in the wire (A)

• = perpendicular distance from the wire to the point (m)

• Right-hand rule: Determines the direction of the magnetic field around a current-carrying wire

Step-by-Step Guidance

1. Draw a diagram showing the positions of the two wires, the direction of their currents, and the location of point P relative to each wire.

2. Calculate the distance from each wire to point P. For wire 2, this is given as 6 cm. For wire 1, add the separation between the wires (9 cm) to the 6 cm distance from wire 2 to P.

3. Use the formula to calculate the magnetic field at point P due to each wire separately. Be careful with units—convert all distances to meters.

4. Determine the direction of each magnetic field at point P using the right-hand rule. Decide if the fields add or subtract based on their directions.

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Q2. The magnetic field calculated at point P points towards the (a) right, (b) left, (c) into the page, (d) out of the page, (e) none of these.

Background

Topic: Direction of magnetic fields from current-carrying wires

This question checks your ability to apply the right-hand rule to determine the direction of the net magnetic field at a point due to multiple wires with currents in different directions.

Key Terms and Concepts

• Right-hand rule for straight wires: Thumb in direction of current, fingers curl in direction of magnetic field lines.

• Superposition principle: The net field is the vector sum of the fields from each wire.

Step-by-Step Guidance

1. For each wire, use the right-hand rule to determine the direction of the magnetic field at point P.

2. Compare the directions from both wires and determine the net direction (into the page, out of the page, left, right, etc.).

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Q3. Calculate the net force per unit length on wire 2. Give the magnitude and direction of the field (net magnetic field near the location of wire 2).

Background

Topic: Force between parallel current-carrying wires

This question tests your understanding of how to calculate the force per unit length between two parallel wires carrying currents, using the magnetic field produced by one wire at the location of the other.

Key Terms and Formulas

• Force per unit length between two wires:

• = currents in wires 1 and 2

• = distance between the wires

• Direction: Use the right-hand rule and consider whether the currents are in the same or opposite directions

Step-by-Step Guidance

1. Identify the values for , , and from the problem statement.

2. Plug these values into the formula to set up the calculation for the force per unit length.

3. Determine the direction of the force (attractive or repulsive) based on the directions of the currents in the two wires.

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Q4. Multiple Choice: A circuit consisting of a battery, a resistor, and a capacitor is shown to the right. If V = 12 V, R = 6 Ω, and the magnitude of the potential drop across the resistor is 8.0 V, what is the magnitude of the potential drop across the capacitor?

Background

Topic: Series circuits and voltage division

This question tests your understanding of how voltage divides across components in a series circuit, specifically between a resistor and a capacitor.

Key Terms and Formulas

• Series circuit: The total voltage is divided among the components.

• Voltage law:

• = voltage across the resistor, = voltage across the capacitor

Step-by-Step Guidance

1. Write the equation for the total voltage in a series circuit: .

2. Substitute the given values for and to solve for .

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Q5. Multiple Choice: The figure to the right shows a cross-sectional view of a current loop. The loop is to be modeled as a bar magnet. Which of the statements below is correct?

Background

Topic: Magnetic dipoles and current loops

This question tests your understanding of the magnetic field produced by a current loop and how it relates to the concept of a bar magnet (north and south poles).

Key Terms and Concepts

• Current loop: Produces a magnetic dipole field similar to a bar magnet.

• Right-hand rule for loops: Curl fingers in direction of current, thumb points to north pole.

Step-by-Step Guidance

1. Identify the direction of current in the loop from the diagram.

2. Apply the right-hand rule to determine which side of the loop acts as the north pole.

3. Match your result to the correct statement among the choices.

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