Physics 202 Study Guide: Circuits, Magnetism, and Electromagnetic Concepts

Q1. Consider the circuit shown in the sketch. What is the current through the 120 V emf?

Background

Topic: DC Circuits and Kirchhoff's Rules

This question tests your understanding of how to analyze a multi-loop circuit using Kirchhoff's rules to find the current through a specific battery.

Key Terms and Formulas

• Kirchhoff's Junction Rule: $\sum I = 0$ (conservation of charge at a junction)

• Kirchhoff's Loop Rule: $\sum V = 0$ (sum of potential differences around a closed loop is zero)

• Ohm's Law: $V = IR$

Step-by-Step Guidance

1. Identify all the emf sources and resistors in the circuit. Note their values and arrangement.

2. Assign current directions in each branch of the circuit. Label them (e.g., $I_1$, $I_2$).

3. Write Kirchhoff's loop equations for each independent loop in the circuit, using the loop rule.

4. Write a junction equation if needed, relating the currents at a node.

5. Set up the system of equations to solve for the current through the 120 V battery.

Try solving on your own before revealing the answer!

Final Answer: 2.0 A, direction as shown in the circuit

By solving the system of equations using Kirchhoff's rules, the current through the 120 V battery is found to be 2.0 A in the direction indicated in the diagram.

Q3. A small object with positive charge $q = 5.00 \times 10^{-6}$ C moves to the right with speed $v = 2.00 \times 10^3$ m/s. At the location of the charge, there is a magnetic field $B = 0.400$ T (into the page). What are the magnitude and direction of the force that the magnetic field exerts on the object?

Background

Topic: Magnetic Force on Moving Charges

This question tests your ability to calculate the magnetic force on a moving charged particle using the right-hand rule and the formula for magnetic force.

Key Terms and Formulas

• Magnetic Force: $F = qvB\sin\theta$

• Right-Hand Rule: Determines the direction of the force for positive charges.

Step-by-Step Guidance

1. Identify the values: $q = 5.00 \times 10^{-6}$ C, $v = 2.00 \times 10^3$ m/s, $B = 0.400$ T.

2. Determine the angle $\theta$ between velocity and magnetic field. Here, velocity is perpendicular to the field ($\theta = 90^\circ$).

3. Plug the values into the formula: $F = qvB\sin\theta$.

4. Use the right-hand rule to find the direction of the force (for positive charge).

Try solving on your own before revealing the answer!

Final Answer: 4.0 \times 10^{-3} N, toward the top of the page

The force is calculated using the formula and the right-hand rule, resulting in a magnitude of $4.0 \times 10^{-3}$ N directed upward.

Q5. A small object with mass $8.00 \times 10^{-6}$ kg and charge $q$ enters a region of uniform magnetic field with magnitude $B = 0.400$ T and direction into the page. At it enters the field, the object is traveling with a velocity of $3.00 \times 10^3$ m/s toward the top of the page. The object travels along a semicircular path in the field and exits the field region at a distance of $0.0800$ m from where it entered. What are the sign and magnitude of the charge of the object?

Background

Topic: Motion of Charged Particles in Magnetic Fields

This question tests your understanding of how a charged particle moves in a magnetic field, specifically the relationship between radius, velocity, mass, and charge.

Key Terms and Formulas

• Radius of Path: $r = \frac{mv}{|q|B}$

• Direction: Use the right-hand rule to determine the sign of the charge based on the path.

Step-by-Step Guidance

1. Identify the values: $m = 8.00 \times 10^{-6}$ kg, $v = 3.00 \times 10^3$ m/s, $B = 0.400$ T, $r = 0.0800$ m.

2. Write the formula for the radius of the path: $r = \frac{mv}{|q|B}$.

3. Rearrange to solve for $|q|$: $|q| = \frac{mv}{rB}$.

4. Use the diagram and right-hand rule to determine the sign of the charge.

Try solving on your own before revealing the answer!

Final Answer: $+3.0 \times 10^{-6}$ C

The charge is positive, as determined by the right-hand rule and the direction of the semicircular path.