To determine the magnitude of the magnetic force acting on a charged particle moving through a magnetic field, we can use the formula for the magnetic force \( F \) on a charged particle: \[ F = qvB \sin(\theta) \] 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 lines (in degrees) ### Step-by-Step Calculation 1. **Identify the given values:** - Charge of the particle, \( q = 2 \, \text{C} \) - Velocity of the particle, \( v = 10 \, \text{m/s} \) - Magnetic field strength, \( B = 0.5 \, \text{T} \) - Angle, \( \theta = 30^\circ \) 2. **Convert the angle to radians (if necessary):** - In this case, we can use the sine function directly with degrees, as most calculators can handle degrees. 3. **Calculate \( \sin(30^\circ) \):** - \( \sin(30^\circ) = 0.5 \) 4. **Substitute the values into the formula:** \[ F = (2 \, \text{C}) \times (10 \, \text{m/s}) \times (0.5 \, \text{T}) \times \sin(30^\circ) \] \[ F = 2 \times 10 \times 0.5 \times 0.5 \] 5. **Perform the multiplication:** \[ F = 2 \times 10 = 20 \] \[ F = 20 \times 0.5 = 10 \] \[ F = 10 \times 0.5 = 5 \, \text{N} \] ### Conclusion The magnitude of the magnetic force acting on the particle is **5 N**. Therefore, the correct option is **B**. ### Explanation of Other Options - **Option A (0 N):** This would imply that there is no force acting on the particle. This is incorrect because the particle is moving through a magnetic field at an angle, which will produce a force. - **Option C (10 N):** This value is derived from the product of charge, velocity, and magnetic field strength without considering the angle. It is incorrect because it does not account for the sine of the angle, which is crucial in determining the actual force when the particle is not moving parallel or perpendicular to the field lines. - **Option D (15 N):** This value does not correspond to any calculation based on the given parameters. It is incorrect as it does not follow from the formula used. ### Revision Summary - The magnetic force on a charged particle is calculated using \( F = qvB \sin(\theta) \). - Always consider the angle between the velocity and the magnetic field when calculating the force. - For \( \theta = 30^\circ \), \( \sin(30^\circ) = 0.5 \). - The final answer for the magnetic force in this scenario is **5 N**.