Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let the extension in the string be x.
Given:
Magnitude of the charges, q = 2.0 × 10−8 C
Separation between the charges, r = (0.1+ x) m
By Coulomb's Law, electrostatic force,
\[F = \frac{1}{4\pi \epsilon_0}\frac{q^2}{r^2}\]
The spring force due to extension x,
Electrostatic force = Spring force
\[\frac{1}{4\pi \epsilon_0} \times \frac{q^2}{\left( x + 0 . 1 \right)^2} = K\left( 0 . 1 + x \right)\]
\[ \Rightarrow \left( 0 . 1 + x \right)^3 = \frac{9 \times {10}^9 \times \left( 2 . 0 \times {10}^{- 8} \right)^2}{{10}^{- 2}}\]
\[ = \frac{36 \times {10}^9 \times {10}^{- 16}}{{10}^{- 2}}\]
\[ = 36 \times {10}^{- 5} \]
\[ \Rightarrow x = 3 . 6 \times {10}^{- 6}\] m
Yes, the assumpton is justified. As two similar charges are present at the ends of the spring so they exert repulsive force on each other.Due to the repulsive force between the charges,an extension x is produced in the spring. Springs are made up of elastic material.When a spring is extended then a restoring force acts on it which is always proportioanal to the extension produced and directed opposite to the direction of applied force.The restoring force depends on the elasticity of the material. When the extension is small then only the restoring force is proportinal to the extension.If the extension s camparable to the natural length of the spring then the restoring force will depend on higher powers of the extension produced.
APPEARS IN
RELATED QUESTIONS
- Two insulated charged copper spheres A and B have their centers separated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is 6.5 × 10−7 C? The radii of A and B are negligible compared to the distance of separation.
- What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?
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`).
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 insulating small spheres are rubbed against each other and placed 1 cm apart. If they attract each other with a force of 0.1 N, how many electrons were transferred from one sphere to the other during rubbing?
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.
Two identical pith balls are charged by rubbing one against the other. They are suspended from a horizontal rod through two strings of length 20 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 small spheres, each with a mass of 20 g, are suspended from a common point by two insulating strings of length 40 cm each. The spheres are identically charged and the separation between the balls at equilibrium is found to be 4 cm. Find the charge on each sphere.
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. Assuming x<<d, show that this force is proportional to x.
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.
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?
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?
Define a unit charge.
A force F acts between sodium and chlorine ions of salt (sodium chloride) when put 1 cm apart in air. The permittivity of air and dielectric constant of water are `epsilon_0` and K respectively. When a piece of salt is put in water, electrical force acting between sodium and chlorine ions 1 cm apart is ____________.
Polarised dielectric is equivalent to ______.
A charge Q is divided into two parts of q and Q – q. If the coulomb repulsion between them when they are separated is to be maximum, the ratio of Q/q should be ______.
Coulomb's law is given by F = k q1q2 rn where n is
Two charges q and – 3q are placed fixed on x-axis separated by distance ‘d’. Where should a third charge 2q be placed such that it will not experience any force?
Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from the mid-point on the perpendicular bisector. The value of x at which charge q will experience the maximum Coulomb's force is ______.
What is meant by the statement: "Relative permittivity of water is 81"?
