The correct option is **D. conductor is at right angle with the field**. ### Detailed Explanation: To understand why the force on a current-carrying conductor in a magnetic field is greatest when the conductor is at a right angle (90 degrees) to the magnetic field, we need to refer to the fundamental principles of electromagnetism, specifically the Lorentz force law. 1. **Lorentz Force Law**: The force \( F \) experienced by a current-carrying conductor in a magnetic field is given by the formula: \[ F = I \cdot L \cdot B \cdot \sin(\theta) \] where: - \( F \) is the magnetic force, - \( I \) is the current flowing through the conductor, - \( L \) is the length of the conductor in the magnetic field, - \( B \) is the magnetic flux density (strength of the magnetic field), - \( \theta \) is the angle between the direction of the current and the direction of the magnetic field. 2. **Understanding the Sine Function**: The sine function, \( \sin(\theta) \), varies between 0 and 1. It reaches its maximum value of 1 when \( \theta = 90^\circ \). This means that the force is maximized when the angle between the conductor and the magnetic field is 90 degrees. - If \( \theta = 0^\circ \) (the conductor is parallel to the magnetic field), then \( \sin(0) = 0 \), and thus \( F = 0 \). No force acts on the conductor. - If \( \theta = 90^\circ \) (the conductor is perpendicular to the magnetic field), then \( \sin(90) = 1\), and the force is maximized. 3. **Physical Interpretation**: When the conductor is perpendicular to the magnetic field, the magnetic field lines exert the maximum influence on the moving charges (electrons) in the conductor. This results in the greatest deflection of the charges, leading to a stronger force acting on the conductor. ### Why the Other Options are Incorrect: - **Option A: Conductor makes an angle of 60° with the field**: - At 60 degrees, \( \sin(60) \) is approximately 0.866. While this is a significant value, it is not the maximum possible value of 1, which occurs at 90 degrees. Therefore, the force is not maximized at this angle. - **Option B: Force is independent of the angles between the fields and the conductor**: - This statement is incorrect because the force is explicitly dependent on the angle \( \theta \) as shown in the Lorentz force equation. The angle directly affects the sine function, which determines the magnitude of the force. - **Option C: Conductor is parallel with the field**: - When the conductor is parallel to the magnetic field (0 degrees), the sine of the angle is zero (\( \sin(0) = 0 \)), resulting in no force acting on the conductor. This is the opposite of what we want for maximum force. ### Summary of Key Points: - The force on a current-carrying conductor in a magnetic field is maximized when the conductor is at a right angle (90 degrees) to the magnetic field. - The relationship between the force, current, magnetic field strength, and angle is described by the Lorentz force law: \( F = I \cdot L \cdot B \cdot \sin(\theta) \). - The sine function reaches its maximum value of 1 at 90 degrees, leading to the greatest force. - Understanding the dependence of force on angle is crucial for solving problems related to magnetic forces on conductors. This thorough understanding will help you tackle similar questions in your physics exams effectively!