Given below are two statements labelled as Assertion (A) and Reason (R )
Assertion (A): Magnetic field on the axial line at a certain distance is twice as compared to that on the equatorial line at the same distance.
Reason(R ) Electric field due to a dipole varies inversely as the cube of the distance.

Options

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

Answer

To solve the question regarding the Assertion (A) and Reason (R), we need to analyze both statements and determine their validity.

### Step 1: Analyze the Assertion (A)
**Assertion (A):** Magnetic field on the axial line at a certain distance is twice as compared to that on the equatorial line at the same distance.

1. **Understanding Magnetic Fields:**
- For a magnetic dipole, the magnetic field (B) at a point on the axial line (along the axis of the dipole) is given by the formula:
\[ B_{\text{axial}} = \frac{\mu_0}{4\pi} \cdot \frac{2M}{r^3} \]
where \(M\) is the magnetic moment and \(r\) is the distance from the center of the dipole.

2. **Magnetic Field on the Equatorial Line:**
- The magnetic field at a point on the equatorial line is given by:
\[ B_{\text{equatorial}} = \frac{\mu_0}{4\pi} \cdot \frac{M}{r^3} \]

3. **Comparing the Two Fields:**
- If we compare the two expressions:
\[ B_{\text{axial}} = 2 \cdot B_{\text{equatorial}} \]
- This confirms that the assertion is true.

### Step 2: Analyze the Reason (R)
**Reason (R):** Electric field due to a dipole varies inversely as the cube of the distance.

1. **Understanding Electric Fields:**
- The electric field (E) due to an electric dipole at a point on the axial line is given by:
\[ E_{\text{axial}} = \frac{2kp}{r^3} \]
where \(k\) is a constant and \(p\) is the dipole moment.

2. **Electric Field on the Equatorial Line:**
- The electric field at a point on the equatorial line is given by:
\[ E_{\text{equatorial}} = \frac{kp}{r^3} \]

3. **Conclusion about the Reason:**
- Both expressions show that the electric field varies inversely with the cube of the distance \(r\). Therefore, the reason is also true.

### Step 3: Conclusion
- Both the Assertion (A) and Reason (R) are true.
- However, the Reason (R) does not explain the Assertion (A) since they pertain to different physical phenomena (magnetic field vs electric field).

### Final Answer:
- Both A and R are true, but R is not the correct explanation of A.

---