To find 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 (in meters, m), - \( \theta \) is the angle between the direction of the magnetic field and the direction of the current (in degrees). ### Step-by-Step Explanation 1. **Identify the Given Values**: - Current, \( I = 5 \, \text{A} \) - Magnetic field strength, \( B = 0.2 \, \text{T} \) - Angle, \( \theta = 30^\circ \) 2. **Determine the Length of the Conductor**: - The problem does not specify the length of the conductor, \( L \). However, we can assume a unit length (1 meter) for the purpose of calculating the force per meter of the conductor. This is a common approach in physics problems unless otherwise stated. 3. **Calculate the Sine of the Angle**: - We need to find \( \sin(30^\circ) \). From trigonometric values, we know: \[ \sin(30^\circ) = 0.5 \] 4. **Substitute the Values into the Formula**: - Now we can substitute the values into the formula: \[ F = BIL \sin(\theta) = (0.2 \, \text{T}) \times (5 \, \text{A}) \times (1 \, \text{m}) \times \sin(30^\circ) \] \[ F = (0.2) \times (5) \times (1) \times (0.5) \] 5. **Perform the Calculation**: - Calculate the force: \[ F = 0.2 \times 5 \times 0.5 = 0.5 \, \text{N} \] ### 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 sine function or miscalculating the product of the values. - **Option C (1.5 N)**: This option is also incorrect. It does not align with the calculations based on the given values and the sine of the angle. - **Option D (2.0 N)**: This option is incorrect as well. It is significantly higher than the calculated force and does not reflect the relationship defined by the formula. ### Common Pitfalls - **Forgetting to use the sine of the angle**: It’s crucial to include \( \sin(\theta) \) in the calculation, as it accounts for the angle between the current and the magnetic field. - **Not using the correct units**: Ensure that all values are in the correct units (A for current, T for magnetic field, m for length). - **Assuming a length without justification**: If the length of the conductor is not given, it’s common to assume a length of 1 meter for calculations. ### Revision Summary - Use the formula \( F = BIL \sin(\theta) \) to calculate magnetic force. - Remember to convert angles to sine values when calculating. - Always check units to ensure consistency. - If length is not specified, assume a unit length (1 m) for calculations.