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 the magnetic field (in meters, m), - \( \theta \) is the angle between the conductor and the magnetic field (in degrees or radians). ### 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 that the length is 1 meter for the purpose of calculating the force per unit length. 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 product step-by-step: \[ F = 0.2 \times 5 = 1.0 \] \[ F = 1.0 \times 1 = 1.0 \] \[ F = 1.0 \times 0.5 = 0.5 \, \text{N} \] ### 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 value is incorrect because it does not account for the sine of the angle. The force is halved due to the angle being 30 degrees. - **Option C (1.5 N)**: This option is also incorrect as it suggests a higher force than what is calculated. It does not follow from the formula with the given values. - **Option D (2.0 N)**: This option is incorrect as it implies a force that is not supported by the calculations. It does not consider the angle's effect on the force. ### Revision Summary - Use the formula \( F = BIL \sin(\theta) \) to calculate magnetic force. - Remember to convert angles to sine values when calculating. - If the length of the conductor is not given, assume it to be 1 meter for calculations. - Always check the units to ensure they are consistent (N, T, A, m).