NEET 2024 — Physics solution

NEET2024Physics

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 $P$ of magnitude, $4 \times 1 0^{- 6}$ Cm, is $\pm 9 \times 1 0^{3}$ V. (Take $\frac{1}{4 π ε _{0}} = 9 \times 1 0^{9}$ SI units)

Reason (R): $V = \pm \frac{2 P}{4 π ε _{0} r ^{2}}$ , 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
A is true but R is false.
B
A is false but R is true.
C
Both A and R are true and R is the correct explanation of A.
D
Both A and R are true and R is NOT the correct explanation of A.

Solution

Axial potential of a dipole: $V = \frac{1}{4 π ε _{0}} \frac{P}{r ^{2}}$ (the $1/ r^{2}$ is correct, but with $P$ in the numerator, not $2 P$ ).

Compute: $V = 9 \times 1 0^{9} \times \frac{4 \times 1 0 ^{- 6}}{2 ^{2}} = \pm 9 \times 1 0^{3}$ V. So A is true.

R is false because the correct formula has $P / r^{2}$ , not $2 P / r^{2}$ .

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