(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.
Obtain the expression for the potential due to an electric dipole of dipole moment p at a point ‘d’ on the axial line.
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 ?
What is the amount of work done in moving a point charge around a circular arc of radius r at the center where another point charge is located ?
Figure shows the field lines due to a positive charge. Is the work done by the field in moving a small positive charge from Q to P, positive or negative? Give reason.
Write two properties of equipotential surfaces. Depict equipotential surfaces due to an isolated point charge. Why do the equipotential surfaces get closer as the distance between the equipotential surfaces and the source charge decreases ?
Calculate the amount of work done to dissociate a system of three charges 1 mC, 1 mC and – 4 mC placed on the vertices of an equilateral triangle of side 10 cm.
(i) An ac source generating a voltage V = V₀ sin ωt is connected to a capacitor of capacitance C. Find the expression of the current I flowing through it.Plot a graph of V and I versus ωt to show that the current is π/2 ahead of the voltage.
(ii) A resistor of 200Ω and a capacitor of 15 µF are connected in series to a 220 V, 50 Hz ac source.Calculate the current in the circuit and the rms
voltage across the resistor and the capacitor. Why the algebraic sum of these voltages is more than the source voltage ?
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) 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.
A device X is connected across an ac source of voltage V = V₀ sin ωt. The current through X is given as I = I₀sin(ωt +π/2).
(a) Identify the device X and write the expression for its reactance.
(b) Draw graphs showing variation of voltage and current with time over one cycle of ac, for X.
(c) How does the reactance of the device X vary with frequency of the ac ? Show this variation graphically.
(d) Draw the phasor diagram for the device X.
(a) Draw graphs showing the variations of inductive reactance and capacitive reactance with frequency of the applied ac source.
(b) Draw the phasor diagram for a series RC circuit connected to an ac source.
(c) An alternating voltage of 220 V is applied across a device X, a current of 0.25 A flows, which lag behind the applied voltage in phase by π/2 radian.If the same voltage is applied across another device Y, the same current flows but now it is in phase with the applied voltage.
(i) Name the devices X and Y.
(ii) Calculate the current flowing in the circuit when the same voltage is applied across the series combination of X and Y.
(i) Prove that current flowing through an ideal inductor connected across ac source, lags the voltage in phase by .
(ii) An inductor of self inductance 100 mH, and a bulb are connected in series with ac source of rms voltage 10V, 50 Hz. It is found that effective voltage of the circuit leads the current in phase by .Calculate the inductance of the inductor used and average power dissipated in the circuit, if a current of 1 A flows in the circuit.
(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.