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 conductor and the magnetic field (in degrees or radians). ### Given Data: - Current, \( I = 5 \, \text{A} \) - Magnetic field strength, \( B = 0.2 \, \text{T} \) - Length of the conductor, \( L = 0.4 \, \text{m} \) - Angle, \( \theta = 90^\circ \) ### Step-by-Step Calculation: 1. **Identify the sine of the angle**: Since the angle \( \theta \) is \( 90^\circ \), we know that: \[ \sin(90^\circ) = 1 \] 2. **Substitute the values into the formula**: \[ F = BIL \sin(\theta) = (0.2 \, \text{T}) \times (5 \, \text{A}) \times (0.4 \, \text{m}) \times 1 \] 3. **Perform the multiplication**: - First, calculate \( B \times I \): \[ 0.2 \, \text{T} \times 5 \, \text{A} = 1.0 \, \text{T} \cdot \text{A} \] - Next, multiply by \( L \): \[ 1.0 \, \text{T} \cdot \text{A} \times 0.4 \, \text{m} = 0.4 \, \text{N} \] 4. **Final Result**: \[ F = 0.4 \, \text{N} \] ### Conclusion: The magnitude of the magnetic force acting on the conductor is **0.4 N**. Therefore, the correct option is **A**. ### Explanation of Other Options: - **Option B (1.0 N)**: This value could be mistakenly calculated if one were to incorrectly multiply the values or misinterpret the angle. However, it does not match our calculations. - **Option C (2.0 N)**: This option might arise from an error in calculating the product of \( B \), \( I \), and \( L \) or misunderstanding the sine function. It is not supported by the calculations. - **Option D (4.0 N)**: This option is significantly higher than the calculated force and suggests a misunderstanding of the relationship between the variables or a miscalculation. ### Common Pitfalls: - Forgetting to convert units or misinterpreting the angle can lead to incorrect results. - Not recognizing that \( \sin(90^\circ) = 1 \) can lead to unnecessary complications in calculations. - Confusing the direction of the force with its magnitude; the formula gives magnitude only. ### Revision Summary: - Use the formula \( F = BIL \sin(\theta) \) to calculate magnetic force. - Ensure to use the correct values for \( B \), \( I \), \( L \), and \( \theta \). - Remember that \( \sin(90^\circ) = 1 \) simplifies calculations. - Check calculations step-by-step to avoid common errors.