To determine 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 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 \( v = 5 \, m/s \) - Magnetic field strength \( B = 0.3 \, T \) - Since the particle is moving perpendicular to the magnetic field, the angle \( \theta = 90^\circ \). 2. **Calculate \( \sin(\theta) \)**: - For \( \theta = 90^\circ \), \( \sin(90^\circ) = 1 \). 3. **Substitute the Values into the Formula**: \[ F = (2 \times 10^{-6} \, C) \cdot (5 \, m/s) \cdot (0.3 \, T) \cdot 1 \] 4. **Perform the Calculation**: \[ F = 2 \times 10^{-6} \cdot 5 \cdot 0.3 \] \[ F = 2 \times 5 \times 0.3 \times 10^{-6} \] \[ F = 3 \times 10^{-6} \, N \] \[ F = 0.000003 \, N = 0.003 \, N \] ### Conclusion The magnitude of the magnetic force acting on the particle is **0.003 N**. Therefore, the correct option is **A**. ### Explanation of Other Options - **Option B (0.03 N)**: This value is incorrect because it suggests a tenfold increase in the force. The calculations show that the force is significantly lower than this value. - **Option C (0.3 N)**: This option is also incorrect as it is an order of magnitude higher than the calculated force. It does not align with the values provided in the problem. - **Option D (0.6 N)**: This option is incorrect as well, being much higher than the calculated force. It does not reflect the relationship between charge, velocity, and magnetic field strength. ### 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 the sine function is crucial when the angle is not 90 degrees. In this case, since the motion is perpendicular, it simplifies the calculation. - **Neglecting the direction of the force**: While this question asks for 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 \( \sin(90^\circ) = 1 \) when the velocity is perpendicular to the magnetic field. - Check calculations carefully to avoid common mistakes in unit conversion and angle interpretation.