Electric Charges and Fields
What is the potential energy of the electric dipole?
The total potential at a point at distance r from their common centre,where r < a, would be:
The distance from A at which both of them produce the same potential is:
|P.||E is independent of d||1.||A point charge Q at the origin|
|Q.||2.||A small dipole with point charges Q at (0, 0, l) and –Q at (0, 0, –l). Take 2l ≪ d|
|R.||3.||An infinite line charge coincident with the x-axis, with uniform linear charge density λ|
|S.||4.||Two infinite wires carrying uniform linear charge density parallel to the x- axis. The one along (y = 0, z = l) has a charge density +λ and the one along (y = 0, z = –l) has a charge density –λ. Take 2l ≪ d|
|5.||Infinite plane charge coincident with the xy-plane with uniform surface charge density|
|List I||List II|
|P.||Q1, Q2, Q3, Q4 all positive||1.||+x|
|Q.||Q1, Q2 positive; Q3, Q4 negative||2.||−x|
|R.||Q1, Q4 positive; Q2, Q3 negative||3.||+y|
|S.||Q1, Q3 positive; Q2, Q4 negative||4.||−y|
Two non-conducting spheres of radii R1 and R2 and carrying uniform volume charge densities +ρ and −ρ, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,
A cubical region of side a has its centre at the origin. It encloses three fixed point charges, −q at, at and −q at. Choose the correct option (s).
An infinitely long solid cylinder of radius R has a uniform volume charge density. It has a spherical cavity of radius R/2 with its centre on the axis cylinder, as shown in the figure. The magnitude of the electric at the Point P, which is at a distance 2R from the axis of the cylinder, is given by the expression. The value of k is
Reason: In a hollow spherical shield, the electric field inside it is zero at every point.
Consider an electric field, where E0 is a constant. The flux through the shaded area (as shown in the figure) due to this field is:
A spherical metal shell A of radius RA and a solid metal sphere B of radius are kept for apart and each is given charge ‘+ Q’. Now they are connected by a thin metal wire. Then
Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side ‘a’. The surface tension of the soap film is . The system of charges and planar film are in equilibrium, and, where ‘k’ is a constant. Then N is
A uniformly charged thin spherical shell of radius R carries uniform surface charge density of per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is proportional to
A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength . When the field is switched off, the drop is observed to fall with terminal velocity . Given g = 9.8ms-2, viscosity of the air = and the density of oil = 900 kg m-3, the magnitude of q is
A few electric field lines for a system of two charges Q1 and Q2 fixed at two different points on the axis are shown in the figure. These lines suggest that
A disk of radius a/4 having a uniformly distributed charge 6C is placed in the x-y plane with its centre at (-a/2, 0,0). A rod of length a carrying a uniformly distributed charge 8C is placed on the
x − axis from x= a/4 to x = 5a/4. Two points charges -7C and 3C are placed at (a/4, -a/4, 0) and (-3a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces . The electrical flux through this cubical surface is
Three concentric metallic spherical shells of radii R, 2R, and 3R are given charges Q1, Q2, Q3 respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, is
Under the influence of the Coulomb field of charge +Q, a charge −q is moving around it in an elliptical orbit. Find out the correct statement(s).
A solid sphere of radius has a charge distributed in its volume with a charge density where and are constants and is the distance from its centre. If the electric field at is 1/8 times that at find the value of
The electric field within the nucleus is generally observed to be linearly dependent on r. This implies.
Consider the charge configuration and a spherical Gaussian surface, as shown in the figure. When calculating the flux of the electric field over the spherical surface, the electric field will be due to
(A) q2 only
(B) only the positive charges
(C) all the charges
(D) +q1 and –q1