Advertisements
Advertisements
Question
Derive an expression for the electric potential at any point along the axial line of an electric dipole.
Advertisements
Solution
Suppose P is a point on the axial position of the dipole.
Length of dipole = 2a
Suppose point P is at the distance 'r' from the center of the dipole.
The potential at a point is V = `1/(4piε_0).Q/r`
So, the potential at P due to q is Vq = `1/(4piε_0).q/(a+r)`
Potential at P due to -q is V-q = `1/(4piε_0).(-q)/(a-r)`
The total potential at P is `V = V_q + V_(-q)`
= `1/(4piε_0).q/((a + r)) + 1/(4piε_0).(-q)/((r - a))`
= `q/(4piε_0)[1/((a + r)) + 1/((a - r))]`
V = `q/(4piε_0).(2a)/((a^2 - r^2))`
APPEARS IN
RELATED QUESTIONS
A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. The potential at a distance of 2 cm from the centre of the sphere is ______.
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 ______.
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:
For \[r \gg a\], applying the Binomial theorem to \[r_1^2 \approx r^2\left(1 - \frac{2a\cos\theta}{r}\right)\] and retaining only first-order terms, the approximation for \[\frac{1}{r_1}\] is:
The exact potential on the axial line of a dipole with half-length l, before applying the approximation \[r \gg l\], is:
Which statement correctly describes the situation for a charge moved along the equatorial line of a dipole?
The exact potential at a general point of a dipole with half-length l, before neglecting the \[l^2\cos^2\theta\] term, is:
In the general formula for the potential due to a dipole, setting θ = 0° and θ = 90° respectively recovers which two special cases?
A water molecule (H₂O) behaves like a natural electric dipole because:
In the binomial-approximation derivation of the dipole potential, which order of terms in \[a/r\] is retained throughout the calculation?
