Advertisements
Advertisements
Question
Two equal charges, 2.0 × 10−7 C each, are held fixed at a separation of 20 cm. A third charge of equal magnitude is placed midway between the two charges. It is now moved to a point 20 cm from both the charges. How much work is done by the electric field during the process?
Solution
Let the third charge be moved from point A to point B.
Magnitude of the charges, q = 2.0 × 10−7 C
Distance of both the charges from point A, r = 10 cm =0.1 m
Distance of both the charges from point B, r' = 20 cm =0.2 m
Potential at A,
\[V_A = 2 \times \frac{1}{4\pi \epsilon_0}\frac{q}{r}\]
Potential at B,
\[V_B = 2 \times \frac{1}{4\pi \epsilon_0}\frac{q}{r'}\]
Work done,
\[\Rightarrow W = 2 \times {10}^{- 7} \left[ \frac{2 \times 2 \times {10}^{- 7}}{4 \pi\epsilon_0}\left( \frac{1}{0 . 1} - \frac{1}{0 . 2} \right) \right]\]
\[ \Rightarrow W = 3 . 6 \times {10}^{- 3}\] J
APPEARS IN
RELATED QUESTIONS
A particle of mass m and charge (−q) enters the region between the two charged plates initially moving along x-axis with speed vx (like particle 1 in the fig.). The length of plate is L and an uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is qEL2/(2m`"v"_"x"^2`).
Does the force on a charge due to another charge depend on the charges present nearby?
At what separation should two equal charges, 1.0 C each, be placed, so that the force between them equals the weight of a 50 kg person?
Two charges 2.0 × 10−6 C and 1.0 × 10−6 C are placed at a separation of 10 cm. Where should a third charge be placed, such that it experiences no net force due to these charges?
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 = 10−10 m and is abbreviated as Å ) with the proton at the centre. The hydrogen atom is said to be in the ground state in this case. Find the magnitude of the electric force between the proton and the electron of a hydrogen atom in its ground state.
Two identical balls, each with a charge of 2.00 × 10−7 C and a mass of 100 g, 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, each carrying a charge q, are suspended from a common point by two strings of equal length l. Find the mass of each ball if the angle between the strings is 2θ in equilibrium.
A particle with a charge of 2.0 × 10−4 C is placed directly below and at a separation of 10 cm from the bob of a simple pendulum at rest. The mass of the bob is 100 g. What charge should the bob be given so that the string becomes loose?
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 rests 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.
Repeat the previous problem if the particle C is displaced through a distance x along the line AB.
Two particles A and B possessing charges of +2.00 × 10−6 C and of −4.00 × 10−6 C, respectively, are held fixed at a separation of 20.0 cm. Locate the points (s) on the line AB, where (a) the electric field is zero (b) the electric potential is zero.
Three identical charges, each with a value of 1.0 × 10−8 C, are placed at the corners of an equilateral triangle of side 20 cm. Find the electric field and potential at the centre of the triangle.
Two charged particles, with equal charges of 2.0 × 10−5 C, are brought from infinity to within a separation of 10 cm. Find the increase in the electric potential energy during the process
Three charges +Q, q, +Q are placed respectively, at distance, 0, d/2 and d from the origin, on the X-axis. If the net force experienced by +Q, placed at x = 0, is zero then value of q is ____________.
The force between two charges 0.06 m apart is 5 N. If each charge is moved towards the other by 0.01 m, then the force between them will become ____________.
Two charges of equal magnitudes kept at a distance r exert a force F on each other. If the charges are halved and distance between them is doubled, then the new force acting on each charge is ______.
The ratio of the forces between two charges placed at a certain distance apart in the air and by the same distance apart in a medium of dielectric constant K is ______.
Four charges equal to - Q are placed at the four a corners of a square and charge q is at its centre. If the system is in equilibrium, the value of q is ______.
What is meant by the statement: "Relative permittivity of water is 81"?
