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?
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
Check that the ratio ke2/G memp is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?
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 ?
Plot a graph showing the variation of coulomb force (F) versus ,`(1/r^2)` where r is the distance between the two charges of each pair of charges: (1 μC, 2 μC) and (2 μC, − 3 μC). Interpret the graphs obtained.
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?
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.
Suppose the second charge in the previous problem is −1.0 × 10−6 C. Locate the position where a third charge will not experience a net force.
Two charged particles are placed 1.0 cm apart. What is the minimum possible magnitude of the electric force acting on each charge?
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.
Suppose an attractive nuclear force acts between two protons which may be written as F=Ce−kr/r2. Suppose that k = 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.
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?
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. 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.
A water particle of mass 10.0 mg and with a charge of 1.50 × 10−6 C stays suspended in a room. What is the magnitude of electric field in the room? What is its direction ?
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
Two particles of masses 5.0 g each and opposite charges of +4.0 × 10−5 C and −4.0 × 10−5 C are released from rest with a separation of 1.0 m between them. Find the speeds of the particles when the separation is reduced to 50 cm.
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 ____________.
Polarised dielectric is equivalent to ______.
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 ______.
Which of the following statements about nuclear forces is not true?
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 ______.
