Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The potential (V) at any axial point, at 2 m distance(r) from the centre of the dipole of dipole moment vector

 \(\vec{P}\) of magnitude, 4 × 10^-6 C m, is ± 9 × 10³ V.
      (Take \(\frac{1}{4\pi\epsilon_0}=9\times10^9\) SI units)
 

Reason R : \(V=±\frac{2P}{4\pi \epsilon_0r^2}\), where r is the distance of any axial point, situated at 2 m from the centre of the dipole.
In the light of the above statements, choose the correct answer from the options given below :

• 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. A is false but R is true.

Answer 1

The Correct Option is C

Step 1: Calculate the Potential on the Axial Line of a Dipole

The formula for the potential at an axial point of a dipole is:

$$ V = \frac{P}{4\pi\epsilon_0 r^2} $$

Where:

\( V \) = Potential

\( P \) = Dipole moment

\( r \) = Distance from the dipole center

\( \epsilon_0 \) = Permittivity of free space

Step 2: Substitute the Given Values

Given:

• \( P = 4 \times 10^{-6} \) Cm
• \( r = 2 \) m
• \( \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \) SI units

Substituting these values:

$$ V = \frac{(4 \times 10^{-6}) \cdot (9 \times 10^9)}{2^2} $$

Solving:

$$ V = \frac{36 \times 10^3}{4} = 9 \times 10^3 \text{ V} $$

This matches the given assertion.

Step 3: Verify the Reason

The reason states the formula:

$$ V = \pm \frac{2P}{4\pi\epsilon_0 r^2} $$

While the formula is correct, the sign ± is used to specify the direction of the potential based on the orientation of the dipole.

However, the potential magnitude was specifically calculated in the assertion, which does not depend on this sign.

Conclusion

Therefore, the reason is unrelated to the assertion.