To determine 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 conductor and the magnetic field. ### Step-by-Step Explanation 1. **Identify the Given Values**: - Current, \( I = 5 \, \text{A} \) - Magnetic field strength, \( B = 0.2 \, \text{T} \) - Length of the conductor, \( L = 0.5 \, \text{m} \) - The angle \( \theta = 90^\circ \) (since the conductor is oriented perpendicular to the magnetic field). 2. **Substituting Values into the Formula**: Since the conductor is perpendicular to the magnetic field, \( \sin(90^\circ) = 1 \). Therefore, the formula simplifies to: \[ F = BIL \] 3. **Calculating the Force**: Now, substituting the known values into the simplified formula: \[ F = (0.2 \, \text{T}) \times (5 \, \text{A}) \times (0.5 \, \text{m}) \] Calculating this step-by-step: - First, calculate \( B \times I \): \[ 0.2 \, \text{T} \times 5 \, \text{A} = 1.0 \, \text{T} \cdot \text{A} \] - Next, multiply by the length \( L \): \[ 1.0 \, \text{T} \cdot \text{A} \times 0.5 \, \text{m} = 0.5 \, \text{N} \] Thus, the magnetic force \( F \) acting on the conductor is: \[ F = 0.5 \, \text{N} \] ### Conclusion The correct answer is **A. 0.5 N**. ### Explanation of Other Options - **Option B (1.0 N)**: This option is incorrect because it assumes either a higher current, a longer length, or a different angle than what was provided. The calculations clearly show that the force is 0.5 N. - **Option C (1.5 N)**: This option is also incorrect for the same reasons as option B. The values provided do not support a force of 1.5 N. - **Option D (2.0 N)**: This option is incorrect as well. The calculations do not yield a force of 2.0 N, and it would require either a higher magnetic field strength or a longer conductor length. ### Common Pitfalls - **Forgetting the Angle**: Always check the angle between the conductor and the magnetic field. If it’s not 90 degrees, you must use the sine function correctly. - **Units**: Ensure that all units are consistent (e.g., current in Amperes, length in meters, magnetic field in Teslas). - **Misinterpretation of the Formula**: Remember that the force is directly proportional to the current, magnetic field strength, and length of the conductor. ### Revision Summary - Use the formula \( F = BIL \sin(\theta) \) to calculate magnetic force. - Ensure the angle is correctly identified; \( \sin(90^\circ) = 1 \). - Substitute values carefully and perform calculations step-by-step. - Check units and ensure they are consistent throughout the calculation.