a 0.2g ball hangs from a thread in a vertical electric field of 3 Newton per coulomb directed upwords the tension in the thread is 4 Newton meter then the charge on the ball is what

To determine the charge on the ball, we can analyze the forces acting on it in the vertical electric field. The ball is subjected to three main forces: the gravitational force pulling it downward, the tension in the thread pulling it upward, and the electric force acting on it due to the electric field. Let's break this down step by step.

Identifying the Forces

First, we need to identify the forces involved:

• Gravitational Force (Weight): This can be calculated using the formula W = mg, where m is the mass of the ball and g is the acceleration due to gravity (approximately 9.81 m/s²).
• Tension (T): This is given as 4 Newtons, acting upward.
• Electric Force (F_e): This is given by the formula F_e = qE, where q is the charge on the ball and E is the electric field strength (3 N/C in this case).

Calculating the Gravitational Force

First, we calculate the weight of the ball:

Given that the mass of the ball is 0.2 g, we convert this to kilograms:

m = 0.2 g = 0.2 / 1000 = 0.0002 kg

Now, we can calculate the weight:

W = mg = 0.0002 kg × 9.81 m/s² = 0.001962 N

Setting Up the Equation

Next, we can set up the equation based on the forces acting on the ball. Since the ball is in equilibrium (not moving), the sum of the forces acting on it must equal zero:

T - W - F_e = 0

Substituting the known values:

4 N - 0.001962 N - qE = 0

We know that E = 3 N/C, so we can rewrite the equation as:

4 N - 0.001962 N - q(3 N/C) = 0

Solving for Charge (q)

Rearranging the equation gives us:

q(3 N/C) = 4 N - 0.001962 N

q(3 N/C) = 3.998038 N

Now, we can solve for q:

q = 3.998038 N / 3 N/C

q ≈ 1.332679 C

Final Result

The charge on the ball is approximately 1.33 coulombs. This value indicates the amount of electric charge that the ball possesses, allowing it to experience a force in the electric field.