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) 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.
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 ?
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.
In a region of constant potential,
(a) the electric field is uniform
(b) the electric field is zero
(c) there can be no charge inside the region
(d) the electric field shall necessarily change, if a charge is placed outside the region
Four point charges Q, q, Q and q are placed at the corners of a square of side ‘a’ as shown in the figure.
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 ?
An electric dipole is placed in a uniform electric field.
(i) Show that no translatory force acts on it.
(ii) Derive an expression for the torque acting on it.
(iii) Find work done in rotating the dipole through 180°.
The potential difference across a resistor ‘r’ carrying current ‘I’ is Ir.
(i) Now if the potential difference across ‘r’ is measured using a voltmeter of resistance ‘’, show that the reading of voltmeter is less than the true value.
(ii) Find the percentage error in measuring the potential difference by a voltmeter.
(iii) At what value of ’, does the voltmeter measures the true potential difference?
Derive an expression for electric field of a dipole at a point on the equatorial plane of the dipole. How does the field vary at large distances?
A source of ac voltage V = V₀ sin ωt, is connected across a pure inductor of inductance L. Derive the expressions for the instantaneous current in the circuit. Show that average power dissipated in the circuit is zero.
A 200 mH (pure) inductor and a 5 µF (pure) capacitor are connected one by one, across a sinusoidal ac voltage source of V = [70.7sin (1000t)] voltage. Obtain the expression for the current in each case.
The figure shows a series LCR circuit with L = 5.0 H, C = 80 µF, R = 40 Ω connected to a variable frequency of 240 V source. Calculate
Four point charges Q, q, Q and q are placed at the corners of a square of side ‘a’ as shown in the figure.