### Correct Option: C. Perpendicular to both the current and the magnetic field ### Detailed Explanation: To understand the direction of the magnetic force experienced by a straight current-carrying conductor in a magnetic field, we can use the **right-hand rule** and the **Lorentz force law**. 1. **Lorentz Force Law**: The magnetic force (\( \mathbf{F} \)) on a current-carrying conductor can be described by the equation: \[ \mathbf{F} = I \mathbf{L} \times \mathbf{B} \] where: - \( I \) is the current flowing through the conductor, - \( \mathbf{L} \) is the length vector of the conductor in the direction of the current, - \( \mathbf{B} \) is the magnetic field vector, - \( \times \) denotes the cross product. 2. **Understanding the Cross Product**: The cross product of two vectors results in a third vector that is perpendicular to the plane formed by the two original vectors. In this case, the direction of the magnetic force is determined by the direction of the current (\( \mathbf{L} \)) and the magnetic field (\( \mathbf{B} \)). 3. **Applying the Right-Hand Rule**: - Point your thumb in the direction of the current (\( I \)). - Point your fingers in the direction of the magnetic field (\( \mathbf{B} \)). - Your palm will then face in the direction of the magnetic force (\( \mathbf{F} \)) acting on the conductor. Since the current and the magnetic field are perpendicular to each other, the resulting magnetic force will also be perpendicular to both the current and the magnetic field. ### Why Other Options Are Incorrect: - **Option A: Parallel to the current** This option is incorrect because the magnetic force cannot be parallel to the current when the magnetic field is perpendicular. The force is always perpendicular to both the current and the magnetic field due to the nature of the cross product. - **Option B: Opposite to the magnetic field direction** This option is also incorrect. The magnetic force does not act in the opposite direction of the magnetic field. Instead, it is determined by the orientation of both the current and the magnetic field, resulting in a force that is perpendicular to both. - **Option D: In the same direction as the magnetic field** This option is incorrect for the same reason as option B. The magnetic force cannot be in the same direction as the magnetic field when the current is perpendicular to it. The force is a result of the interaction between the current and the magnetic field, leading to a direction that is perpendicular to both. ### Summary of Key Points: - The magnetic force on a current-carrying conductor in a magnetic field is given by the Lorentz force law. - The direction of the force can be determined using the right-hand rule. - The force is always perpendicular to both the direction of the current and the magnetic field. - The correct answer is that the magnetic force is **perpendicular to both the current and the magnetic field**. ### Revision Summary: - The magnetic force on a current-carrying conductor is given by \( \mathbf{F} = I \mathbf{L} \times \mathbf{B} \). - Use the right-hand rule to determine the direction of the magnetic force. - The force is always perpendicular to both the current and the magnetic field. - The correct answer is option C: Perpendicular to both the current and the magnetic field.