Advertisements
Advertisements
प्रश्न
A long cylindrical volume contains a uniformly distributed charge of density ρ. Find the electric field at a point P inside the cylindrical volume at a distance x from its axis (see the figure).
उत्तर
Given:-
Volume charge density inside the cylinder = ρ
Let the radius of the cylinder be r.
Let charge enclosed by the given cylinder be Q
Consider a Gaussian cylindrical surface of radius x and height h.
Let charge enclosed by the cylinder of radius x be q'.
The charge on this imaginary cylinder can be found by taking the product of the volume charge density of the cylinder and the volume of the imaginary cylinder. Thus, q' = ρ( π x2 h)
From Gauss's Law,
`oint "E" . "ds" = ("q"_"en")/∈_0`
`"E" . 2 pi "xh" = (ρ( pi "x"^2 "h"))/ ∈_0`
`"E" = (ρ"x")/(2∈_0)`
APPEARS IN
संबंधित प्रश्न
A polythene piece rubbed with wool is found to have a negative charge of 3 × 10−7 C.
(a) Estimate the number of electrons transferred (from which to which?)
(b) Is there a transfer of mass from wool to polythene?
Write the expression for the displacement current in terms of the rate of change of electric flux.
A proton and an electron are placed in a uniform electric field.
Two large conducting plates are placed parallel to each other and they carry equal and opposite charges with surface density σ as shown in the figure. Find the electric field (a) at the left of the plates (b) in between the plates and (c) at the right of the plates.
A positive charge Q is distributed uniformly over a circular ring of radius R. A particle of mass m, and a negative charge q, is placed on its axis at a distance x from the centre. Find the force on the particle. Assuming x << R, find the time period of oscillation of the particle if it is released from there .
A positive charge q is placed in front of a conducting solid cube at a distance d from its centre. Find the electric field at the centre of the cube to the charges appearing on its surface.
Choose the correct option.
An electron is placed between two parallel plates connected to a battery. If the battery is switched on, the electron will
Two small spheres 18 cm apart have equal negative charges and repel each other with the force of 6 × 10-3 N. Find the total charge on both spheres.
One metallic sphere A is given a positive charge whereas another identical metallic sphere B of exactly the same mass as A is given an equal amount of negative charge. Then
When 1019 electrons are removed from a neutral metal plate through some process, the electric charge on it is ______
Two small conducting spheres of equal radius have charges +10 µC and -20 µC respectively and placed at a distance R from each other experience force F1· If they are brought in contact and separated to the same distance, they experience force F2. The ratio of F1 to F2 is ____________.
Equal charge are given to two-sphere of different radii. The potential will be
A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength 1 × 105 NC–1. If the charge on the particle is 40 μC and the initial velocity is 200 ms-1, how much distance it will travel before coming to the rest momentarily ______.
Given below are two statements:
- Statement I: The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle.
- Statement II: The electric force accelerates the positively charged particle perpendicular to the direction of the electric field. The magnetic force accelerates the moving charged particle along the direction of the magnetic field.
In light of the above statements, choose the most appropriate answer from the options given below.
A charge of 4 µC is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be:
Two identical conducting spheres with negligible volume have 2.1 nC and -0.1 nC charges, respectively. They are brought into contact and then separated by a distance of 0.5 m. The electrostatic force acting between the spheres is ______ × 10-9N.
[Given: 4πε0 = `1/(9xx10^9)` SI unit]
