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The electric field at the origin is along the positive x-axis. A small circle is drawn with the center at the origin cutting the axes at points A, B, C and D having coordinates (α, 0), (0, α), (–α, 0), (0, –α) respectively. Out of the points on the periphery of the circle, the potential is minimum at
Suppose all the electrons of 100g water are lumped together to form a negatively charged particle and all the nuclei are lumped together to form a positively charged particle. If these two particles are placed 10.0 cm away from each other, find the force of attraction between them. Compare it with your weight.
NaCl molecule is bound due to the electric force between the sodium and the chlorine ions when one electron of sodium is transferred to chlorine. Taking the separation between the ions to be 2.75 × 10–8 cm, find the force of attraction between them. State the assumptions (if any) that you have made.
Suppose an attractive nuclear force acts between two protons which may be written as F = CE–kx/r2.
(a) Write down the dimensional formulae and appropriate SI units of C and κ.
(b) Suppose that κ = 1 fermi–1 and that the repulsive electric force between the protons is just balanced by the attractive nuclear force when the separation is 5 fermi. Find the value of C.
A hydrogen atom contains one proton and one electron. It may be assumed that the electron revolves in a circle of radius 0.53 angstrom (1 angstrom = 10–19 m and is abbreviated as ) with the proton at the center. The hydrogen atom is said to be in the ground sate in this case. Find the magnitude of the electric force between the proton and the electron of a hydrogen atom in its ground state.
Ten positively charged particles are kept fixed on the x-axis at points x = 10 cm, 20 cm 30 cm, …., 100 cm. The first particle has a charge 1.0 × 10–8 C, the second 8 × 10–8 C, the third 27 × 10–8 C and so on. The tenth particle has a charge 1000 × 10–8 C. Find the magnitude of the electric force acting on a 1C charge placed at the origin.
Two identical balls, having a charge of 2.00 × 10–7 C and a mass of 100g, are suspended from a common point by two insulating strings each 50 cm long. The balls are held at a separation 5.0 cm apart and then released. Find
(a) the electric force on one of the charged balls
(b) the components of the resultant force on it along and perpendicular to the string
(c) the tension in the string
(d) the acceleration of one of the balls. Answers are to be obtained only for the instant just after the release.
Two identical pith balls are charged by rubbing against each other. They are suspended from a horizontal rod through two strings of length20 cm each, the separation between the suspension points being 5 cm. In equilibrium, the separation between the balls is 3 cm. Find the mass of each ball and the tension in the strings. The charge on each ball has a magnitude 2.0 × 10–8 C.
Two Particles A and B having charges q and 2q respectively are placed on a smooth table with a separation d. A third particle C is to be clamped on the table in such a way that the particles A and B remain at rest on the table under electrical forces. What should be the charge on C and where should it be clamped?
Two identically charged particles are fastened to the two ends of a spring of spring constant 100 N m–1 and natural length 10 cm. The system resets on a smooth horizontal table. If the charge on each particle is 2.0 × 10–8 C, find the extension in the length of the spring. Assume that the extension is small as compared to the natural length. Justify this assumption after you solve the problem.
A particle A having a charge of 2.0 × 10–6 C is held fixed on a horizontal table. A second charged particle of mass 80g stays in equilibrium on the table at a distance of 10 cm from the first charge. The coefficient of friction between the table and this second particle is μ = 0.2. Find the range within which the charge of this second particle may lie.
Two particles A and B, each carrying a charge Q, are held fixed with a separation d between them. A particle C having mass m and charge q is kept at the middle point of the line AB.
(a) If it is displaced through a distance x perpendicular to AB, what would be the electric force experienced by it.
(b) Assuming x << d, show that this force is proportional to x.
(c) Under what conditions will the particle C execute simple harmonic motion if it is released after such a small displacement?
Find the time period of the oscillations if these conditions are satisfied.
Positive charge Q is distributed uniformly over a circular ring of radius R. A particle having a mass m and a negative charge q, is placed on its axis at a distance x from the centre. Find the force on the particle. Assuming x <<R, find the time period of oscillation of the particle if it is released from there.
A particle of mass 1g and charge 2.5 × 10–4 C is released from rest in an electric field of 1.2 × 104 N C–1.
(a) Find the electric force and the force of gravity acing on this particle. Can one of these forces be neglected in comparison with the other for approximate analysis?
(b) How long will it take for the particle to travel a distance of 40 cm?
(c) What will be the speed of the particle after travelling this distance?
(d) How much is the work done by the electric force on the particle during this period?
A block of mass m containing a net positive charge q is placed on a smooth horizontal table which terminates in a vertical wall as shown in figure. The distance of the block from the wall is d. A horizontal electric field E towards right is switched on. Assuming elastic collisions (if any) find the time period of the resulting oscillatory motion. Is it a simple harmonic motion?
An electric field of 20 N C–1 exists along the x-axis in space. Calculate the potential difference VB – VA where the points A and B are given by,
(a) A = (0, 0); B = (4m, 2m)
(b) A = (4m, 2m); B = (6m, 5m)
(c) A = (0, 0); B = (6m, 5m)
Do you find any relation between the answers of parts (a), (b) and (c)?
An electric field of magnitude 1000 NC–1 is produced between two parallel plates having a separation of 2.0 cm as shown in figure.
(a) What is the potential difference between the plate?
(b) With what minimum speed should an electron be projected from the lower plate in the direction of the field so that it may reach the upper plate?
(c) Suppose the electron is projected from the lower plate with the speed calculated in part (b). The direction of projection makes an angle of 60° with the field. Find the maximum height reached by the electron.
A uniform field of 2.0 NC–1 exists in space in x-direction.
(a) Taking the potential at the origin to be zero, write an expression for the potential at a general point (x, y, z).
(b) At which points, the potential is 25 V?
(c) If the potential at the origin is taken to be 100 V, what will be the expression for the potential at ta general point?
(d) What will be the potential at the origin if the potential at infinity is taken to be zero? Is it practical to choose the potential at infinity to be zero?
Two particles A and B, having opposite charges 2.0 × 10–6 C and –2.0 × 10–6 C, are placed at a separation of 1.0 cm.
(a) Write down the electric dipole moment of this pair.
(b) Calculate the electric field at a point on the axis of the dipole 1.0 m away from the center.
(c) Calculate the electric field at a point on the perpendicular bisector of the dipole and 1.0 m sway from the center.
Two particles, carrying –q and +q and having equal masses m each, are fixed at the ends of a light rod of length a to form a dipole. The rod is clamped at an end and is placed in a uniform electric field E with the axis of the dipole along the electric field. The rod is slightly tilted and then released. Neglecting gravity find the time period of small oscillations.