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
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.
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?
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. 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 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 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 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 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?
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 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 ?
Explain in detail Coulomb’s law and its various aspects.
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 ____________.
Two positive charges ______.
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
The S.I unit of electric permittivity 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?
Which of the following statements about nuclear forces is not true?
