Advertisements
Advertisements
प्रश्न
A particle A with a charge of 2.0 × 10−6 C is held fixed on a horizontal table. A second charged particle of mass 80 g 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.
उत्तर
Given:
Magnitude of charge of particle A, q1 = 2.0 × 10−6 C
Separation between the charges, r = 0.1 m
Mass of particle B, m = 80 g = 0.08 kg
Let the magnitude of charge of particle B be q2.
By Coulomb's Law, force on B due to A,
\[F = \frac{1}{4\pi \epsilon_0}\frac{q_1 q_2}{r^2}\]
Force of friction on B = μmg
Since B is at equilibrium,
Coulomb force = Frictional force
⇒ F = μmg
\[ \Rightarrow \frac{9 \times {10}^9 \times 2 \times {10}^{- 6} \times q_2}{\left( 0 . 1 \right)^2} = 0 . 2 \times 0 . 08 \times 9 . 8\]
\[ \Rightarrow q_2 = 8 . 71 \times {10}^{- 8} C\]
∴ The range of the charge = ∓ 8.71×10-8 C
APPEARS IN
संबंधित प्रश्न
Four charges +q, −q, +q and −q are to be arranged respectively at the four corners of a square ABCD of side 'a'.
(a) Find the work required to put together this arrangement.
(b) A charge q0 is brought to the centre of the square, the four charges being held fixed. How much extra work is needed to do this ?
One end of a 10 cm long silk thread is fixed to a large vertical surface of a charged non-conducting plate and the other end is fastened to a small ball of mass 10 g and a charge of 4.0× 10-6 C. In equilibrium, the thread makes an angle of 60° with the vertical. Find the surface charge density on the plate.
Find the electric force between two protons separated by a distance of 1 fermi (1 fermi = 10−15 m). The protons in a nucleus remain at a separation of this order.
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−kr/r2. Write down the dimensional formulae and appropriate SI units of C and k.
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 particles A and B, each carrying a charge Q, are held fixed with a separation dbetween them. A particle C of mass m and charge q is kept at the middle point of the line AB. If it is displaced through a distance x perpendicular to AB, what would be the electric force experienced by it?
A point charge produces an electric field of magnitude 5.0 NC−1 at a distance of 40 cm from it. What is the magnitude of the charge?
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 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?
Solve numerical example.
Three equal charges of 10×10-8 C respectively, each located at the corners of a right triangle whose sides are 15 cm, 20 cm, and 25cm respectively. Find the force exerted on the charge located at the 90° angle.
What are the differences between the Coulomb force and the gravitational force?
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 ____________.
Two-point charges of + 0.2 µµC and -0.2 µµC are separated by 1 o8 m. What is the value of the electric field at an axial point at a distance of 0.1 m from their mid-point?
A total charge Q is broken in two parts Q1 and Q2 and they are placed at a distance R from each other. The maximum force of repulsion between them will occur, when ____________.
For charges q1 and q2 separated by a distance R the magnitude of the electrostatic force is given by ______.
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 ______.
A spring of spring constant 5 × 103 N/m is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is:
What is meant by the statement: "Relative permittivity of water is 81"?
