Advertisements
Advertisements
प्रश्न
Using Gauss’s law, prove that the electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it.
उत्तर
Consider a uniformly charged infinite plane sheet of charge density σ.
We have to find electric field E at point as shown in figure.
Now, we construct a Gaussian surface as shown in figure in the form of cylinder.
Applying Gauss’s Law,
`phi =oint vecE*dvecs =(σΔs)/in_0`
`=> E Deltas + EDelta +0 = (sigma Deltas)/in_0`
`= 2EDeltas = (sigma Deltas)/(in_0)`
`=> E = sigma /(2in_0)`
It shows that electric field is uniform due to charged infinite plane sheet. Also, we can say that E is independent from distance from the sheet.
APPEARS IN
संबंधित प्रश्न
Use Gauss's law to find the electric field due to a uniformly charged infinite plane sheet. What is the direction of field for positive and negative charge densities?
Find the electric field intensity due to a uniformly charged spherical shell at a point (ii) inside the shell. Plot the graph of electric field with distance from the centre of the shell.
Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.0 × 10−22 C/m2. What is E:
- in the outer region of the first plate,
- in the outer region of the second plate, and
- between the plates?
An infinitely large thin plane sheet has a uniform surface charge density +σ. Obtain the expression for the amount of work done in bringing a point charge q from infinity to a point, distant r, in front of the charged plane sheet.
Using Gauss's law in electrostatics, deduce an expression for electric field intensity due to a uniformly charged infinite plane sheet. If another identical sheet is placed parallel to it, show that there is no electric field in the region between the two sheets ?
A point object is placed on the principal axis of a convex spherical surface of radius of curvature R, which separates the two media of refractive indices n1 and n2 (n2 > n1). Draw the ray diagram and deduce the relation between the object distance (u), image distance (v) and the radius of curvature (R) for refraction to take place at the convex spherical surface from rarer to denser medium.
A spherical shell made of plastic, contains a charge Q distributed uniformly over its surface. What is the electric field inside the shell? If the shell is hammered to deshape it, without altering the charge, will the field inside be changed? What happens if the shell is made of a metal?
A large non-conducting sheet M is given a uniform charge density. Two uncharged small metal rods A and B are placed near the sheet as shown in the following figure.
(a) M attracts A.
(b) M attracts B.
(c) A attracts B.
(d) B attracts A.
“A uniformly charged conducting spherical shell for the points outside the shell behaves as if the entire charge of the shell is concentrated at its centre”. Show this with the help of a proper diagram and verify this statement.
