### Correct Option: A **Explanation:** The magnetic force (\( \mathbf{F} \)) acting on a charged particle moving in a magnetic field is described by the Lorentz force law, which states: \[ \mathbf{F} = q(\mathbf{v} \times \mathbf{B}) \] Where: - \( \mathbf{F} \) is the magnetic force, - \( q \) is the charge of the particle, - \( \mathbf{v} \) is the velocity vector of the particle, - \( \mathbf{B} \) is the magnetic field vector, - \( \times \) denotes the cross product. From this equation, we can see that the magnetic force is directly proportional to: 1. The magnitude of the charge (\( q \)). 2. The magnitude of the velocity (\( v \)). 3. The strength of the magnetic field (\( B \)). 4. The sine of the angle (\( \theta \)) between the velocity vector and the magnetic field vector, which is implicit in the cross product. Thus, the magnetic force depends on both the charge and the velocity of the particle, confirming that option A is correct. ### Why Other Options Are Incorrect: - **Option B: Independent of the magnitude of the charge** - This option is incorrect because the magnetic force is explicitly dependent on the charge of the particle. If the charge were zero, the force would also be zero, which contradicts the statement that it is independent of the charge. - **Option C: Proportional to the velocity \( v \) only** - This option is misleading because while the magnetic force does depend on the velocity, it is not solely dependent on it. The force also depends on the charge and the magnetic field. Therefore, saying it is proportional to velocity only ignores the other critical factors. - **Option D: Proportional to the magnitude of the charge only** - This option is incorrect for the same reason as option C. The magnetic force is not only dependent on the charge but also on the velocity of the particle and the magnetic field. Thus, it cannot be said to be proportional to the charge alone. ### Summary of Key Points: - The magnetic force on a charged particle is given by the equation \( \mathbf{F} = q(\mathbf{v} \times \mathbf{B}) \). - The force is proportional to both the charge \( q \) and the velocity \( v \) of the particle. - The direction of the force is determined by the right-hand rule, which involves the cross product of the velocity and magnetic field vectors. - Understanding the dependencies of the magnetic force is crucial for solving problems related to charged particles in magnetic fields. ### Common Pitfalls: - Forgetting that the magnetic force is a vector quantity, which means it has both magnitude and direction. - Confusing the magnetic force with electric force, which has different dependencies. - Not considering the angle between the velocity and magnetic field when calculating the force, as it affects the magnitude of the force through the sine function in the cross product.