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 (in Newtons, N) - \( q \) is the charge of the particle (in Coulombs, C) - \( v \) is the velocity of the particle (in meters per second, m/s) - \( B \) is the magnetic field strength (in Teslas, T) - \( \theta \) is the angle between the velocity of the particle and the magnetic field (in degrees or radians) ### Step-by-Step Calculation 1. **Identify the given values:** - Charge \( q = +2 \, \mu C = 2 \times 10^{-6} \, C \) - Velocity \( v = 5 \, m/s \) - Magnetic field strength \( B = 0.3 \, T \) - Angle \( \theta = 90^\circ \) 2. **Convert the angle to radians if necessary:** - Since \( \sin(90^\circ) = 1 \), we can directly use this value in our calculations. 3. **Substitute the values into the formula:** \[ F = (2 \times 10^{-6} \, C) \cdot (5 \, m/s) \cdot (0.3 \, T) \cdot \sin(90^\circ) \] \[ F = (2 \times 10^{-6}) \cdot 5 \cdot 0.3 \cdot 1 \] 4. **Perform the multiplication:** - First, calculate \( 2 \times 10^{-6} \cdot 5 = 10 \times 10^{-6} = 1 \times 10^{-5} \) - Then, multiply by \( 0.3 \): \[ F = 1 \times 10^{-5} \cdot 0.3 = 0.3 \times 10^{-5} = 3 \times 10^{-6} \, N \] 5. **Convert to standard form:** \[ F = 0.00003 \, N = 0.03 \, N \] ### Conclusion The magnitude of the magnetic force acting on the particle is **0.03 N**. Therefore, the correct option is **C**. ### Explanation of Other Options - **Option A (0.003 N)**: This value is too low. It likely results from a miscalculation or misunderstanding of the charge or the multiplication involved. - **Option B (0.015 N)**: This value is also incorrect. It may arise from incorrectly calculating the product of the charge, velocity, and magnetic field strength. - **Option D (0.05 N)**: This value is too high. It could be a result of miscalculating the multiplication or misunderstanding the relationship between the variables. ### Common Pitfalls - **Forgetting to convert units**: Always ensure that the charge is in Coulombs, velocity in m/s, and magnetic field strength in Teslas. - **Misunderstanding the angle**: Remember that \( \sin(90^\circ) = 1 \). If the angle were different, you would need to calculate \( \sin(\theta) \) accordingly. - **Neglecting the direction of the force**: While this question focuses on magnitude, it's important to remember that the direction of the magnetic force is given by the right-hand rule. ### Revision Summary - Use the formula \( F = q \cdot v \cdot B \cdot \sin(\theta) \) to calculate magnetic force. - Ensure all units are consistent (C, m/s, T). - Remember that \( \sin(90^\circ) = 1 \) simplifies calculations. - Check calculations step-by-step to avoid common errors.