To find the magnitude of the magnetic force acting on a charged particle moving in a magnetic field, we can use the formula for the magnetic force \( F \) on a charged particle: \[ F = q \cdot v \cdot B \cdot \sin(\theta) \] Where: - \( F \) is the magnetic force, - \( q \) is the charge of the particle, - \( v \) is the velocity of the particle, - \( B \) is the magnetic field strength, - \( \theta \) is the angle between the velocity vector and the magnetic field vector. ### Step-by-Step Calculation 1. **Identify the Given Values**: - Charge \( q = +2 \, \mu C = 2 \times 10^{-6} \, C \) - Velocity \( v = 3 \times 10^6 \, m/s \) - Magnetic field strength \( B = 0.5 \, T \) - Since the particle is moving perpendicular to the magnetic field, \( \theta = 90^\circ \). 2. **Calculate \( \sin(\theta) \)**: - For \( \theta = 90^\circ \), \( \sin(90^\circ) = 1 \). 3. **Substitute the Values into the Formula**: \[ F = (2 \times 10^{-6} \, C) \cdot (3 \times 10^6 \, m/s) \cdot (0.5 \, T) \cdot 1 \] 4. **Perform the Multiplication**: - First, calculate \( 2 \times 3 = 6 \). - Then, multiply \( 6 \) by \( 0.5 \): \[ 6 \cdot 0.5 = 3 \] - Now, combine with the powers of ten: \[ F = 3 \times 10^{-6} \cdot 10^6 = 3 \, N \] 5. **Final Result**: - The magnitude of the magnetic force acting on the particle is \( 0.003 \, N \) or \( 3 \, mN \). ### Conclusion The correct option is **A. 0.003 N**. ### Explanation of Other Options - **B. 0.003 µN**: This is incorrect because \( 0.003 \, N \) is equal to \( 3 \, mN \) or \( 3,000 \, µN \). This option underestimates the force by a factor of 1,000. - **C. 0.03 N**: This is incorrect because it is ten times larger than the calculated force. It suggests a misunderstanding of the multiplication of the charge, velocity, and magnetic field. - **D. 0.3 N**: This is also incorrect as it is an order of magnitude larger than the correct answer. It indicates a possible error in the calculation or misunderstanding of the units. ### Common Pitfalls - **Misunderstanding Units**: Be careful with microcoulombs (µC) and their conversion to coulombs (C). Remember that \( 1 \, µC = 10^{-6} \, C \). - **Forgetting the Angle**: Always check the angle between the velocity and magnetic field. If they are perpendicular, \( \sin(90^\circ) = 1 \) simplifies the calculation. - **Calculation Errors**: Double-check multiplication and powers of ten to avoid simple arithmetic mistakes. ### Revision Summary - Use the formula \( F = q \cdot v \cdot B \cdot \sin(\theta) \) for magnetic force. - Ensure correct unit conversions (e.g., µC to C). - Remember that \( \sin(90^\circ) = 1 \) when the velocity is perpendicular to the magnetic field. - Check calculations carefully to avoid common arithmetic errors.