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Question
A point P lies at a distance x from the midpoint of an electric dipole on its axis. The electric potential at point P is proportional to ______.
Options
`1/x^2`
`1/x^3`
`1/x^4`
`1/x^{1"/"2}`
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Solution
A point P lies at a distance x from the midpoint of an electric dipole on its axis. The electric potential at point P is proportional to `underlinebb(1/x^2)`.
Explanation:
The electric potential of the dipole is given by:
V = `(pcostheta)/(4piε_0r^2)`,
where r is the position vector with respect to the midpoint of the dipole and θ is the angle between r and p (dipole moment). Therefore, the electric potential at a point that lies at a distance x from the midpoint of the dipole will be proportional to `1/r^2`.
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RELATED QUESTIONS
Derive an expression for the electric potential at any point along the axial line of an electric dipole.
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 cm, is ±9 × 103 V.
(Take `1/(4 pi epsilon_0)` = 9 × 109 SI units)
Reason (R): V = `+- (2 vec P)/(4 pi epsilon_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:
Assertion A: The potential (V) at any axial point, at 2 m distance (r) from the centre of the dipole of dipole moment vector of magnitude, 4 × 10−6 Cm, is ± 9 × 103 V. (Take = 9 × 109 SI units)
Reason R: 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:
The electrostatic potential at a general point at distance r from the center of a dipole, making an angle θ with the dipole axis (for r >> a), is:
Since \[p\cos\theta = \vec{p} \cdot \hat{r}\], the dipole potential at a point (r >> a) written in compact vector form is:
At an axial point of an electric dipole (θ = 0° or 180°), the potential is:
The electric potential at any point on the equatorial line of a dipole (θ = 90°) is:
Which statement correctly describes the situation for a charge moved along the equatorial line of a dipole?
In the general formula for the potential due to a dipole, setting θ = 0° and θ = 90° respectively recovers which two special cases?
At an axial point located on the side of the negative charge (θ = 180°), the potential due to the dipole is:
