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 ?
(i) Obtain the expression for the potential to show due to a point charge.
(ii) Potential, due to an electric dipole (length 2a) varies as the ‘inverse square’ of the distance of the ‘field point’ from the centre of the dipole for r > a.
(i) Two isolated metal spheres A and B have radii R and 2R respectively, and same charge q. Find which of the two spheres have greater :
(a) capacitance and
(b) energy density just outside the surface of the spheres.
(ii) (a) Show that the equipotential surfaces are closed together in the regions of strong field and far apart in the regions of weak field. Draw equipotential surfaces for an electric dipole.
(b) Concentric equipotential surfaces due to a charged body placed at the centre are shown. Identify the polarity of the charge and draw the electric field lines due to it.
Two point charges q and –q are located at points (0, 0, – a) and (0, 0, a) respectively.
(i) Find the electrostatic potential at (0, 0, z) and (x, y, 0).
(ii) How much work is done in moving a small test charge from the point (5,0,0) to (– 7, 0, 0) along the x-axis ?
(iii) How would your answer change if the path of the test charge between the same points is not along the x-axis but along any other random path ?
(iv) If the above point charges are now placed in the same positions in the uniform external electric field what would be the potential energy of the charge system in its orientation of unstable equilibrium ?
Justify your answer in each case.
A capacitor of 4 μF is connected as shown in the circuit Figure. The internal resistance of the battery is 0.5 Ω. The amount of charge on the capacitor plates will be :