(A): Electric current density is a vector
(R): A physical quantity having magnitude and direction should be always a vector.

Options

A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
C. (A) is true but (R) is false
D. Both (A) and (R) are false

Answer

To solve the question, we need to analyze both statements provided:

**Step 1: Analyze Statement A**
- Statement A asserts that "Electric current density is a vector."
- Electric current density (denoted as \( \mathbf{J} \)) is defined as the amount of electric current flowing per unit area. Mathematically, it can be expressed as:
\[ \mathbf{J} = \frac{I}{A} \]
where \( I \) is the electric current and \( A \) is the area through which the current flows.
- Since electric current density has both magnitude (the amount of current per unit area) and direction (the direction of current flow), it is indeed a vector quantity.
- Therefore, Statement A is **True**.

**Step 2: Analyze Statement R**
- Statement R states that "A physical quantity having magnitude and direction should always be a vector."
- While it is true that vectors have both magnitude and direction, not all physical quantities that have magnitude and direction are vectors. For example, electric current has a magnitude (like 12 amperes) and a direction (the direction of flow), but it is not classified as a vector quantity.
- Thus, Statement R is **False**.

**Step 3: Conclusion**
- Based on the analysis:
- Statement A is True.
- Statement R is False.
- Therefore, the correct option is that A is true but R is false.

### Final Answer:
The correct answer is: **A is true but R is false.**

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