Correct Option
The correct option is Both A and R are true but R is NOT the correct explanation of A
Explanation
A magnetic field is a physical field that exerts a magnetic force on moving electric charges, electric currents, and magnetic materials. It is mathematically defined at every point in space by both magnitude and direction.
Statement-wise Analysis
- Assertion (A): Correct. A magnetic field is a vector quantity because it possesses both magnitude (strength) and direction. The direction of the magnetic field at any point is the direction of the force acting on a hypothetical North pole placed at that point.
- Reason (R): Correct. Magnetic field lines are a graphical representation of the magnetic field. One of the fundamental properties of these lines is that their relative density (closeness) indicates the strength of the field. The field is stronger where the lines are crowded (closer together) and weaker where they are spaced apart.
Logic of the Explanation
While both statements are factually true, the Reason (R) does not explain the Assertion (A). The fact that field lines are drawn closer to represent higher strength is a convention of the graphical representation. It does not define why the magnetic field is a vector quantity. The vector nature is intrinsic to the field because the force exerted has a specific direction, whereas the density of lines merely visualizes the magnitude component.
Key Takeaway: A physical quantity is a vector if it has both magnitude and direction. Magnetic field lines are visual tools where the tangent gives the direction and the density gives the relative magnitude.