What must be the charge on each pair of pith balls suspended in air form same point by string 10cm long if they repel each other to a seperation of 8 cm?mass of each pith ball is 2grm and g is 10ms-2?

Question

Answer

Charge on Pith Balls Suspended in Air

Given:

Length of string (l) = 10 cm

Separation between pith balls (r) = 8 cm

Mass of each pith ball (m) = 2 g

Acceleration due to gravity (g) = 10 m/s^2

Formula:

Electric Force (F) = k * (q1 * q2) / r^2

Gravitational Force (F) = G * (m1 * m2) / r^2

Electric Field (E) = F / q

Electric Potential (V) = k * q / r

Charge on pith balls (q) = m * g * l / (4 * pi * epsilon * r^2)

Calculations:

Electric Force (F) = Gravitational Force (F)

k * (q^2) / r^2 = G * (m^2) / r^2

q^2 = (G * m^2) / k

q = sqrt((G * m^2) / k)

Charge on each pith ball (q) = m * g * l / (4 * pi * epsilon * r^2)

Answer:

Charge on each pith ball = 6.99 * 10^-7 C

Explanation:

When the pith balls are suspended in air from the same point by a string, they will repel each other due to the presence of like charges on them. The Coulomb's law states that the electric force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. This law is used to calculate the charge on each pith ball.

Initially, the pith balls are at a separation of 10 cm. When they are charged, they repel each other and move away to a separation of 8 cm. The gravitational force between the pith balls is negligible compared to the electric force, so we can equate the two forces and solve for the charge on each pith ball.

The charge on each pith ball is calculated using the formula for Coulomb's law and the definition of electric field. The mass of each pith ball and the acceleration due to gravity are given, so we can use them to find the charge on each pith ball.

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