Two pith balls equally charged and each with a mass of 1.5. White one ball is suspended by a thread, the other is brought close to it and a state of equilibrium is reached. In that situation, the two balls are separated by 2.6cm and the thread attached to the suspended ball makes an angle of 20deg with the vertical. Calculate the charge on each of the pith balls

10000

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14000

To calculate the charges on the pith balls, we can use Coulomb's Law, which states that the electrical force between two charged objects is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Let's go step by step to solve this problem:

Step 1: Find the angle the thread makes with the vertical.
The problem states that the thread attached to the suspended ball makes an angle of 20° with the vertical. This angle will help us in calculating the forces acting on the charged pith balls.

Step 2: Calculate the tension in the thread.
The tension in the thread is equal to the weight of the suspended ball. Since both pith balls have the same mass of 1.5 grams (assuming mass is given in grams), we can find the tension using the formula:
Tension = Mass × Gravity

Step 3: Resolve the tension into horizontal and vertical components.
The vertical component of the tension will balance the weight of the suspended ball, while the horizontal component of the tension will provide the force required to maintain equilibrium between the two charged pith balls.

Step 4: Find the electrostatic force between the two charged pith balls.
The horizontal component of tension should balance the electrostatic force between the two charged pith balls. We can use Coulomb's Law to calculate this force:
Electrostatic Force = (k × Q1 × Q2) / r^2

Step 5: Equate the electrostatic force to the horizontal component of tension.
Since the electrostatic force and the horizontal component of tension are balanced in the state of equilibrium, we can set them equal to each other:
Electrostatic Force = Horizontal Component of Tension

Step 6: Solve for the charge on each pith ball.
Rearranging the equation from step 5, we can solve for the charges on each pith ball:
Q1 = (Tension × r^2) / (k × sin(angle))
Q2 = (Tension × r^2) / (k × sin(angle))

We can now substitute the given values into the formula to calculate the charge on each pith ball.