Advertisements
Advertisements
प्रश्न
- 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?
Advertisements
उत्तर
(a) 
Charge on sphere A, qA = Charge on sphere B, qB = 6.5 × 10−7 C
Distance between the spheres, r = 50 cm = 0.5 m
Force of repulsion between the two spheres,
`"F" = ("q"_"A""q"_"B")/(4piin_0r^2)`
Where,
∈0 = Free space permittivity
`1/(4piin_0) = 9 xx 10^9 "N m"^2 "C"^-2`
∴ `"F" = (9 xx 10^9 xx (6.5 xx 10^-7)^2)/((0.5)^2)`
= 1.52 × 10−2 N
Therefore, the force between the two spheres is 1.52 × 10−2 N.
(b) After doubling the charge, charge on sphere A, qA = Charge on sphere B, qB = 2 × 6.5 × 10−7 C = 1.3 × 10−6 C
The distance between the spheres is halved.
∴ `"r" = 0.5/2`
= 0.25 m
Force of repulsion between the two spheres,
`F = ("q"_"A" "q"_"B")/(4 pi ∈_0 r^2)`
= `(9 xx 10^9 xx 1.3 xx 10^-6 xx 1.3 xx 10^-6)/(0.25)^2`
= 16 × 1.52 × 10-2
= 0.243 N
Therefore, the force between the two spheres is 0.243 N.
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 ?
A charge of 1.0 C is placed at the top of your college building and another equal charge at the top of your house. Take the separation between the two charges to be 2.0 km. Find the force exerted by the charges on each other. How many times your weight is this force?
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?
Four equal charges of 2.0 × 10−6 C each are fixed at the four corners of a square of side 5 cm. Find the Coulomb's force experienced by one of the charges due to the other three.
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 1 C charge placed at the origin.
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 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.
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.
A particle A with a charge of 2.0 × 10−6 C and a mass of 100 g is placed at the bottom of a smooth inclined plane of inclination 30°. Where should another particle B, with the same charge and mass, be placed on the incline so that it may remain in equilibrium?
Repeat the previous problem if the particle C is displaced through a distance x along the line AB.
Two identical particles, each with a charge of 2.0 × 10−4 C and mass of 10 g, are kept at a separation of 10 cm and then released. What would be the speed of the particles when the separation becomes large?
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.
Write down Coulomb’s law in vector form and mention what each term represents.
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 ____________.
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 ______.
The electric force acting between two point charges kept at a certain distance in vacuum is 16 N. If the same two charges are kept at the same distance in a medium of dielectric constant 8, the electric force acting between them is ____________ N.
The ratio of the forces between two small spheres with constant charge (a) in air (b) in a medium of dielectric constant K is ______.
Identify the wrong statement in the following.
Coulomb's law correctly describes the electric force that ______.
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?
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 ______.
