Advertisements
Advertisements
Question
In case of an infinite line charge, how does intensity of electric field at a point change, if at all, when.
- charge on it is doubled?
- distance of the point is halved?
Advertisements
Solution
The intensity of the electric field E at a point located at a distance r from the line charge is `E = λ/(2π∈_0r)` where, λ is the charge per unit length.
- The charge on it is doubled.
Given λ = 2λ
∴ E' = `λ/(2π∈_0r)`
New electric field intensity
E' = `(2λ)/(2π∈_0r)`
= `2⋅ λ/(2π∈_0r)`
= 2E
Thus, the intensity of the electric field is doubled. - The distance of the point is halved:
Given, r' = `r/2`
∴ E' = `λ/(2π∈_0r"'")`
New electric field intensity
E' = `λ/(2π∈_0(r/2))`
= `2⋅λ/(2π∈_0r)`
= 2E
Hence, the intensity of the electric field is also doubled in this case.
APPEARS IN
RELATED QUESTIONS
A charge is distributed uniformly over a ring of radius 'a'. Obtain an expression for the electric intensity E at a point on the axis of the ring. Hence, show that for points at large distance from the ring, it behaves like a point charge.
The bob of a simple pendulum has a mass of 40 g and a positive charge of 4.0 × 10−6 C. It makes 20 oscillations in 45 s. A vertical electric field pointing upward and of magnitude 2.5 × 104 NC−1 is switched on. How much time will it now take to complete 20 oscillations?
A hemisphere is uniformly charged positively. The electric field at a point on a diameter away from the centre is directed ______.
A solid sphere of radius R has a charge Q distributed in its volume with a charge density ρ = kra, where k and a are constants and r is the distance from its centre. If the electric field at r = `"R"/2` is `1/8` times that at r = R, the value of a is ______.
An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is ______.
Electric field at a point varies as r° for ______.
Electric lines of force about negative point charge are ______
Two equal point charges of the same sign are fixed on the y-axis, on either side of the origin equidistant from it, with the distance between them d. A third charge moves along the x-axis. The distance of the third charge from either of the two fixed charges when force on the third charge is maximum will be ______ cm.
[d = 10 cm]
Consider two identical point charges located at points (0, 0) and (a, 0).
Is there a point on the line joining them at which the electric field is zero?
Point charge of 10 µC is placed at the origin. At what location on the X-axis should a point charge of 40 µC be placed so that the net electric field is zero at x = 2 cm on the X-axis?
