A:Current density is a very is a vector quantity .
R : Electric current , passing through a given unit area is current density.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion , then mark
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion then mark.
C. If Assertion is ture statement but Reason is false , then mark
D. If both Assertion and Reason are false statements then mark.

Answer

To solve the question regarding the assertion (A) and reason (R) about current density, we will analyze both statements step by step.

### Step 1: Understanding Current Density
**Assertion (A):** Current density is a vector quantity.

**Reason (R):** Electric current, passing through a given unit area is current density.

**Explanation:**
- Current density (denoted as **J**) is defined as the amount of electric current (**I**) flowing per unit area (**A**) of a cross-section. Mathematically, it is expressed as:
\[ J = \frac{I}{A} \]

### Step 2: Analyzing the Nature of Current Density
- Current density is indeed a vector quantity. This is because it has both magnitude and direction. The direction of current density is the same as the direction of the flow of positive charge (conventional current).

### Step 3: Understanding the Components of Current Density
- The current can be expressed in terms of charge density (**n**), charge of the carriers (**e**), drift velocity (**V_d**), and cross-sectional area (**A**):
\[ I = n \cdot e \cdot A \cdot V_d \]
- When we substitute this into the formula for current density, we get:
\[ J = \frac{I}{A} = \frac{n \cdot e \cdot A \cdot V_d}{A} = n \cdot e \cdot V_d \]
- Here, **V_d** (drift velocity) is a vector quantity, which indicates that **J** is also a vector quantity since it is proportional to **V_d**.

### Step 4: Direction of Current Density
- The direction of current density is defined as normal to the surface through which the current is flowing. This means that if you have a wire and you take a cross-section, the current density vector will point in the direction of the current flow, which is perpendicular to the surface of the wire.

### Conclusion
- Both the assertion and reason are correct. However, the reason does not provide a complete explanation of why current density is a vector quantity. Therefore, the answer to the question is that both statements are true, but the reason is not a correct explanation of the assertion.

### Final Answer:
- The assertion (A) is true, and the reason (R) is also true, but R is not a correct explanation of A. Thus, the answer is option 2.