To determine the magnitude of the magnetic force acting on a straight conductor carrying a current in a magnetic field, we can use the formula: \[ F = BIL \sin(\theta) \] Where: - \( F \) is the magnetic force (in Newtons, N), - \( B \) is the magnetic field strength (in Teslas, T), - \( I \) is the current (in Amperes, A), - \( L \) is the length of the conductor within the magnetic field (in meters, m), - \( \theta \) is the angle between the direction of the current and the direction of the magnetic field. ### Step-by-Step Calculation 1. **Identify the Given Values**: - Current, \( I = 5 \, \text{A} \) - Magnetic field strength, \( B = 0.2 \, \text{T} \) - Length of the conductor, \( L = 0.5 \, \text{m} \) - Orientation: The conductor is perpendicular to the magnetic field, so \( \theta = 90^\circ \). 2. **Calculate the Sine of the Angle**: - Since the conductor is perpendicular to the magnetic field, \( \sin(90^\circ) = 1 \). 3. **Substitute the Values into the Formula**: \[ F = BIL \sin(\theta) = (0.2 \, \text{T}) \times (5 \, \text{A}) \times (0.5 \, \text{m}) \times 1 \] 4. **Perform the Calculation**: \[ F = 0.2 \times 5 \times 0.5 = 0.5 \, \text{N} \] ### Conclusion The magnitude of the magnetic force acting on the conductor is **0.5 N**. Therefore, the correct option is **A**. ### Explanation of Other Options - **Option B (1.0 N)**: This option is incorrect because it suggests that the force is double the calculated value. This could arise from a misunderstanding of the formula or miscalculating the product of the values. - **Option C (1.5 N)**: This option is also incorrect. It does not correspond to any logical combination of the given values and indicates a significant miscalculation. - **Option D (2.0 N)**: This option is incorrect as well. It suggests an even larger force, which is not supported by the values provided. ### Common Pitfalls - **Misunderstanding the Angle**: Always ensure that the angle used in the sine function corresponds to the actual orientation of the conductor relative to the magnetic field. - **Forgetting to Use the Correct Units**: Ensure that all values are in the correct units (A for current, T for magnetic field strength, m for length). - **Neglecting the Sine Function**: If the angle is not 90 degrees, remember to calculate the sine of the angle correctly. ### Revision Summary - Use the formula \( F = BIL \sin(\theta) \) to calculate the magnetic force. - Ensure the angle \( \theta \) is correctly identified; \( \sin(90^\circ) = 1 \) for perpendicular orientation. - Substitute the values carefully and perform the multiplication step-by-step. - Double-check calculations to avoid common pitfalls related to angles and units.