Question

1.
Two small spheres 18 cm apart have
equal negative charges and repel each
other with the force of 6x10 N. Find the
total charge on both spheres.​

Answer 1

Correct Question:-

Two small spheres 18 cm apart have

equal negative charges and repel each

other with the force of 6x10^-8 N. Find the total charge on both spheres.

Answer:-

$\red{\bigstar}$ Total charges $\large\leadsto\boxed{\rm\green{-9.28 \times 10^{-10} \: C}}$

• Given:-

Separation of the two spheres = 18 cm = 0.18 m

Repulsive force between the spheres= 6x10^-8 N

• To Find:-

The total charge on both spheres.

• Solution:-

We know,

$\pink{\bigstar}$ $\large\underline{\boxed{\bf\purple{F = \dfrac{kqQ}{r^2}}}}$

where,

F = Repulsive force

k = Coulomb's constant

q = charge on 1st sphere

Q = charge on 2nd sphere

r = separation between the spheres

Given that, both the spheres have equal negative charge.

Hence,

★ q = Q

• Substituting the values in Formula:-

→ $\sf 6 \times 10^{-8} = \dfrac{9 \times 10^{9} \times (q)^2}{(0.18)^2}$

→ $\sf (q)^2 = \dfrac{6 \times 10^{-8} \times (0.18)^2}{9 \times 10^9}$

→ $\sf (q)^2 = \dfrac{2 \times 10^{-8} \times 0.0324}{3 \times 10^{9}}$

→ $\sf (q)^2 = 0.67 \times 10^{-17} \times 0.0324$

→ $\sf (q)^2 = 0.0216 \times 10^{-17}$

→ $\sf (q)^2 = 0.216 \times 10^{-18}$

→ $\sf q = \sqrt{0.216 \times 10^{-18}}$

→ $\sf q = 0.464 \times 10^{-9}$

→ $\sf q = 4.64 \times 10^{-10}\: C$

The charges are negative.

Hence,

★ $\large\boxed{\bf\pink{- 4.64 \times 10^{-10} \: C}}$

Charge on one sphers is -4.64 × 10^-10 C.

Therefore,

• Total charge = 2q

★ $\large\boxed{\bf\pink{- 9.28 \times 10^{-10} \: C}}$

Answer 2

Given :

• Spheres, r = 18cm = 18 × 10^-2 m = 0.18 m

• repulsive force acting between them, F = 6 × 10^-8 N

To Find :

• Find the total charge on both spheres.

Solution :

Using Coulomb's law,

• Coulomb's law states that the force between two point charges are directly proportional to the product of charges and inversely proportional to the square of distance between them.

• It states that the force of attraction or repulsion between two point charges varies inversely as the sqaure of the distance between the charges and is propotional to the product of 2 charges.

• F = kq²/r²

Substitute all values :

6 × 10^-8 = 9 × 10^9 × q²/(0.18)²

(2/3) × 10^-17 × (0.18)² = q²

q² = 0.0216 × 10^-17

q² = 0.216 × 10^-18

q² = 0.46 × 10^-9

q² = 0.46 nC

• hence, charge on each sphere is -0.46n C