A test charge q is moved without acceleration from A to C along the path from A to B and then from B to C in electric field E as shown in the figure.
Two closely spaced equipotential surfaces A and B with potentials V and V + , (where is the change in V), are kept distance apart as shown in the figure. Deduce the relation between the electric field and the potential gradient between them. Write the two important conclusions concerning the relation between the electric field and electric potentials.
Two point charges q and –2q are kept d distance apart. Find the location of the point relative to charge q at which potential due to this system of charges is zero.
Three concentric metallic shells A, B and C of radii a, b and c (a < b < c) have surface charge densities +σ, –σ and +σ respectively as shown in the figure.
N spherical droplets, each of radius r, have been charged to have a potential V each. If all these droplets were to coalesce to form a single large drop, what would be the potential of this large drop ?
(It is given that the capacitance of a sphere of radius x equals
Find the P.E. associated with a charge q if it were present at the point P with respect to the ‘setup’ of two charged spheres, arranged as shown. Here O is the mid-point of the line O1O2.
Two point charges q1 and q2 are located at and respectively in an external electric field E. Obtain the expression for the total work done in assembling this configuration.
(i) Write two properties by which electric potential is related to the electric field.
(ii) Two point charges q₁ and q₂ separated by a distance of r₁₂ are kept in an external electric field. Derive an expression for the potential energy of the system of two charges in the field.
(i) Derive the expression for the electric potential due to an electric dipole at a point on its axial line.
(ii) Depict the equipotential surface due to electric dipole.
Define an equipotential surface. Draw equipotential surfaces :
(i) in the case of a single point charge and
(ii) in a constant electric field in z-direction. Why the equipotential surfaces about a single charge are not equidistant ?
(iii) Can electric field exist tangential to an equipotential surface ? Give reason.
Obtain the expression for the potential due to an electric dipole of dipole moment p at a point ‘d’ on the axial line.
Four point charges Q, q, Q and q are placed at the corners of a square of side ‘a’ as shown in the figure.
(i) Three point charges q, – 4q and 2q are placed at the vertices of an equilateral triangle ABC of side ‘l’ as shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the charge q.
A particle, having a charge +5 µC, is initially at rest at the point x = 30 cm on the x-axis. The particle begins to move due to the presence of a charge Q that is kept fixed at the origin. Find the kinetic energy of the particle at the instant it has moved 15 cm from its initial position if
(a) Q = +15 µC and
(b) Q = – 15 µC
Derive an expression for potential due to a dipole for distances large compared to the size of the dipole. How is the potential due to dipole different from that due to single charge ?