To determine the maximum force acting on a conductor carrying a current in a magnetic field, we can use the formula: \[ F = BIL \sin(\theta) \] Where: - \( F \) is the force in newtons (N), - \( B \) is the magnetic flux density in teslas (T), - \( I \) is the current in amperes (A), - \( L \) is the length of the conductor in meters (m), - \( \theta \) is the angle between the direction of the magnetic field and the direction of the current. ### Step-by-Step Explanation 1. **Identify the Given Values**: - Length of the conductor, \( L = 2 \, \text{m} \) - Current, \( I = 0.8 \, \text{A} \) - Magnetic flux density, \( B = 0.5 \, \text{T} \) 2. **Determine the Angle**: - The maximum force occurs when the angle \( \theta \) is 90 degrees (i.e., when the conductor is perpendicular to the magnetic field). At this angle, \( \sin(90^\circ) = 1 \). 3. **Substitute the Values into the Formula**: - Since we are looking for the maximum force, we can set \( \sin(\theta) = 1 \): \[ F = BIL \sin(90^\circ) = BIL \] \[ F = (0.5 \, \text{T}) \times (0.8 \, \text{A}) \times (2 \, \text{m}) \] 4. **Calculate the Force**: \[ F = 0.5 \times 0.8 \times 2 \] \[ F = 0.5 \times 1.6 = 0.8 \, \text{N} \] ### Conclusion The maximum force acting on the conductor is **0.8 N**. Therefore, the correct option is **B**. ### Explanation of Other Options - **Option A: 0.2 N**: This value is too low. It may arise from a misunderstanding of the formula or incorrect substitution of values. - **Option C: 3.2 N**: This value could be mistakenly calculated by incorrectly multiplying the values or assuming a different angle. - **Option D: 8.0 N**: This value is significantly higher than expected and likely results from a miscalculation or misunderstanding of the relationship between the variables. ### Common Pitfalls - **Forgetting the Angle**: Always remember that the angle affects the force calculation. The maximum force occurs at 90 degrees. - **Incorrect Units**: Ensure that all units are consistent (e.g., meters for length, amperes for current, teslas for magnetic flux density). - **Misapplication of the Formula**: Make sure to use the correct formula and understand each component's role in the calculation. ### Revision Summary - The force on a conductor in a magnetic field is given by \( F = BIL \sin(\theta) \). - Maximum force occurs at \( \theta = 90^\circ \) where \( \sin(90^\circ) = 1 \). - For the given values, the maximum force is calculated as \( 0.8 \, \text{N} \). - Always check units and ensure correct application of the formula to avoid common mistakes.