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 4×10⁻⁶ C m, is ±9×10³ V. (Take 1/(4πε₀)=9×10⁹ SI units)…

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 ⃗P of magnitude 4×10⁻⁶ C m, is ±9×10³ V. (Take 1/(4πε₀)=9×10⁹ SI units)
Reason R: V=±(2P)/(4πε₀ r²), 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:

Accepted Answer

(1) A is true but R is false.. The potential of a short dipole at distance r and angle θ from its axis is V=(kP cos θ)/(r²), with k=1/(4πε₀). On the axis θ=0° or 180°, so V=±(kP)/(r²). V=±(9×10⁹×4×10⁻⁶)/(2²)=±9×10³ V, so A is true. R carries a factor of 2 that belongs to the axial field E=(2kP)/(r³). It would give ±1.8×10⁴ V, so R is false.

Step-by-step solution

Why the other options are wrong