The correct option for the question is **C. Perpendicular to both the current and the magnetic field**. ### Detailed Explanation: When a straight conductor carrying an electric current is placed in a magnetic field, it experiences a magnetic force. The direction of this force can be determined using the **right-hand rule**, which is a fundamental concept in electromagnetism. #### Step-by-Step Explanation: 1. **Understanding the Setup**: - You have a straight conductor (like a wire) through which an electric current (I) is flowing. - This conductor is placed in a uniform magnetic field (B) that is perpendicular to the direction of the current. 2. **Applying the Right-Hand Rule**: - To find the direction of the magnetic force (F) acting on the conductor, you can use the right-hand rule: - Point your thumb in the direction of the current (I). - Point your fingers in the direction of the magnetic field (B). - Your palm will then face in the direction of the magnetic force (F) acting on the conductor. - Since the current and the magnetic field are perpendicular to each other, the force will also be perpendicular to both. 3. **Mathematical Representation**: - The force on the conductor can also be calculated using the formula: \[ F = I \cdot L \cdot B \cdot \sin(\theta) \] where: - \( F \) is the magnetic force, - \( I \) is the current, - \( L \) is the length of the conductor in the magnetic field, - \( B \) is the magnetic field strength, - \( \theta \) is the angle between the current direction and the magnetic field direction. - In this case, since the current and magnetic field are perpendicular, \( \theta = 90^\circ \) and \( \sin(90^\circ) = 1 \). Thus, the formula simplifies to: \[ F = I \cdot L \cdot B \] - This shows that the force is dependent on the current, the length of the conductor, and the strength of the magnetic field, but importantly, it confirms that the direction of the force is perpendicular to both the current and the magnetic field. 4. **Why Other Options Are Incorrect**: - **A. Along the direction of the magnetic field**: This is incorrect because the magnetic force does not act in the same direction as the magnetic field. Instead, it acts perpendicular to it. - **B. Opposite to the direction of the current**: This is also incorrect. The magnetic force does not act directly opposite to the current; it is perpendicular to both the current and the magnetic field. - **D. Indeterminate without knowing the strength of the current**: While the magnitude of the force depends on the current strength, the direction of the force can be determined without knowing the current's strength. The right-hand rule gives us the direction regardless of the current's magnitude. ### Revision Summary: - The magnetic force on a current-carrying conductor in a magnetic field is determined using the right-hand rule. - The force is always perpendicular to both the direction of the current and the magnetic field. - The formula for the magnetic force is \( F = I \cdot L \cdot B \) when the current and magnetic field are perpendicular. - Understanding the relationship between current, magnetic field, and force is crucial in electromagnetism.