A small 2g plastic ball is suspended by a 20 cm long string in a uniform electric field. If the ball is in equilibrium when the string makes a 15 degree angle with the vertical, what is the net charge on the ball? E=10^3 N/c(answer: 5.25x10^-6)

Work:
I know E=q/r^2
10^3=q/(.2m)(cos15)

The answer depends upon the direction of the applied electric field. Is it horizontal?

Let's assume that it is, and that the string tenston force is T. In that case
T cos 15 = M g
T sin 15 = Q E
tan 15 = Q E/(M g) = 0.268
g is the acceleration of gravity and M is the mass.
Solve for Q . Make sure M is in kg

The length of the string does not matter, but the angle does.

To find the net charge on the ball, we can start by using the equation E = q / r^2, where E is the electric field strength, q is the net charge on the ball, and r is the distance from the center of the ball to the point in the electric field where the ball is suspended.

Given that the electric field strength E is 10^3 N/C (Newtons per Coulomb) and the distance r is 0.2 m (meters), we can plug these values into the equation:

10^3 N/C = q / (0.2 m)^2

Now, we need to consider the angle that the string makes with the vertical. Since the ball is in equilibrium, we can assume that the vertical component of the tension force in the string must be equal to the weight of the ball.

The weight of the ball can be calculated using the equation Fg = mg, where Fg is the weight, m is the mass of the ball, and g is the acceleration due to gravity (which we assume to be 9.8 m/s^2).

The mass of the ball is given as 2g (grams), which we need to convert to kilograms by dividing by 1000:

m = 2g / 1000 = 0.002 kg

So, the weight of the ball is:

Fg = (0.002 kg) * (9.8 m/s^2) = 0.0196 N

Now, we can consider the forces acting on the ball when it is in equilibrium. There are two forces: the electric force due to the net charge q and the tension force in the string.

Taking the vertical component of the forces, we have:

Tension force (T) * cos(15) = Weight of the ball (Fg)

Since the ball is in equilibrium, the tension force (T) in the string is equal to the electric force:

T = qE

Now we can substitute the values and solve for the net charge q:

qE * cos(15) = Fg

q * (10^3 N/C) * cos(15) = 0.0196 N

q = (0.0196 N) / [(10^3 N/C) * cos(15)]

Evaluating this expression:

q ≈ 5.25 × 10^-6 C

So, the net charge on the ball is approximately 5.25 × 10^-6 Coulombs.

What if the electric field is not horizontal?

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