Advertisements
Advertisements
प्रश्न
Answer the following question.
Derive an expression for the electric field at any point on the equatorial line of an electric dipole.
Advertisements
उत्तर
Electric field for points on the equator plane
The magnitude of the electric field due to two charges +q and –q is
`E_(+q) = q/(4piε_0)1/(r^2 + a^2)`
`E_(-q) = q/(4piε_0)1/(r^2 + a^2)`
`E_(+q) = E_(-q)`
The directions of `E_(+q) and E_(-q)`, are as shown in the figure. The components normal to the dipole axis cancel away. The components along the dipole axis add up.
Total electric field, `E = -(E_(+q) + E_(-q)) costheta hatp` ......(Negative sign shows that the field is opposite to `hatp`)
`E = -(2qa)/(4piε_0(r^2 + a^2)^(3/2))hatp` ...(iii)
At large distance (r >> a), this reduces to,
`E = -(2qa)/(4piε_0r^3)hatp`
`vecp = q xx 2vecahatp`
`E = -vecp/(4piε_0r^3)` ....(r >> a)
संबंधित प्रश्न
Drive the expression for electric field at a point on the equatorial line of an electric dipole.
It is said that the separation between the two charges forming an electric dipole should be small. In comparison to what should this separation be small?
Two particles, carrying charges −q and +q and and of mass m each, are fixed at the ends of a light rod of length a to form a dipole. The rod is clamped at an end and is placed in a uniform electric field E with the axis of the dipole along the electric field. The rod is slightly tilted and then released. Neglecting gravity, find the time period of small oscillations.
When an electric dipole p is placed in a uniform electric field E then at what angle the value of torque will be maximum?
A conic surface is placed in a uniform electric field E as shown in the figure such that the field is perpendicular to the surface on the side AB. The base of the cone is of radius R, and the height of the cone is h. The angle of the cone is θ.
Find the magnitude of the flux that enters the cone's curved surface from the left side. Do not count the outgoing flux (θ < 45°)
Electric dipole consists of two charges of magnitude 0.1 µC separated by a distance of 2 cm. The dipole is in 5 an external field of 105 N/C. What maximum torque does the field exert on the dipole?
Two charges –q each are fixed separated by distance 2d. A third charge q of mass m placed at the mid-point is displaced slightly by x(x << d) perpendicular to the line joining the two fixed charged as shown in figure. Show that q will perform simple harmonic oscillation of time period.
`T = [(8pi^3 ε_0 md^3)/q^2]^(1/2)`
Eight dipoles of charges of magnitude e each are placed inside a cube. The total electric flux coming out of the cube will be ______.
In an electric dipole, what is the locus of a point having zero potential?
Arrangement of an oxygen ion and two hydrogen ions in a water molecule is shown in the figure below.
Calculate the electric dipole moment of a water molecule. Express your answer in terms of e (charge on hydrogen ions), l and θ.
