Two equal small spheres each weighing 1g , hang by two equal silk threads from the same point. The spheres are charged when in contact and come to rest with their centres 2cm apart and 20cm vertically below the point of support. Find the charge on each sphere.

### Asked by ishantkundu31 | 14th Jun, 2021, 05:00: PM

###
Figure shows forces acting on charged sphere. Weight mg is acting downward. Repulsive electrostatic force is shown as F_{e} .
Tension force T acting along string is resolved as ( T cosθ ) and ( T sinθ ) .

(Tcosθ) component balances weight mg. (T sinθ) component balances Electrostatic force F_{e} .
T cosθ = mg ...................... (1)

T sinθ = F_{e} ........................(2)
If we eliminate tension T in above equations, we get , F_{e} = m g tanθ .......................(3)
Eqn.(3) is written as
K × ( q^{2} / d^{2} ) = ( m g tanθ ) ........................... (4)
where K = 1/( 4 π ε_{o} ) = 9 × 10^{9} N m^{2 }C^{-2} Coulomb's constant and d = 2 cm is the distance between charged spheres.
m is mass of sphere , g is acceleration due to gravity and θ is the angle made by the string with vertical
From eqn.(4) , we get

_{e}.

_{e}.

_{e}........................(2)

_{e}= m g tanθ .......................(3)

^{2}/ d

^{2}) = ( m g tanθ ) ........................... (4)

_{o}) = 9 × 10

^{9}N m

^{2 }C

^{-2}Coulomb's constant and d = 2 cm is the distance between charged spheres.

### Answered by Thiyagarajan K | 14th Jun, 2021, 09:41: PM

## Concept Videos

- the force between two charges at distance r is f what will be the force between these charges if the distance between them is doubled and charges are placed in a medium of dielectric constant 10 ?
- A point charge qa = + 100 c is placed at point a (1, 0, 2) m and another point charge qb = +200c isplaced at point b (4, 4, 2) m. Find :(i) magnitude of electrostatic interaction force acting between them(ii) find a f(force on a due to
- Two identical metal spheres have charges +15μC and +25μC areseparated by a distance. If the spheres are first brought into contact and then separated to the original distance, then the ratio of the new force to the previous force is
- two bodies of masses m,2m and charges q and 2q ,q is hanged with two strings of equal length 'l' as shown. which one of the following is correct.
- staate columbs law in vectoe form and explain it
- What is coulombs law
- Q - 10
- Q - 14
- A certain charge Q is divided into two parts q and Q − q, which are then separated by a certain distance. What must q be in terms of Q to maximize the electrostatic repulsion between the two charges?

### Kindly Sign up for a personalised experience

- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions

#### Sign Up

#### Verify mobile number

Enter the OTP sent to your number

Change