A small 9g plastic ball is suspended by a 35 cm long string in a uniform electric field 1110 N/C as shown. The ball is in equilibrium when the string makes a 23 degree angle with the vertical.

what is deta? Maybe you mean Theta, the angle.

Draw a force diagram, qE along the horizontal, and mg downward.

is Tan Theta= qE/mg ?

Find the relationship among deta,mg, and qE.

To understand why the ball is in equilibrium, we need to consider the forces acting on it and how they balance out.

The ball is in an electric field with a magnitude of 1110 N/C. Electric fields exert a force on charged objects. Since the ball is made of plastic, it is an insulator and does not hold any charge. Therefore, the ball does not experience any force due to the electric field.

The only force acting on the ball is the tension in the string. The tension force always acts along the length of the string. When the string is at an angle to the vertical, this tension force can be resolved into two components: one acting vertically upward and one acting horizontally.

Since the ball is in equilibrium, the vertical component of the tension force must balance the weight of the ball. The weight of the ball is equal to the mass of the ball multiplied by the acceleration due to gravity (9.8 m/s^2).

To find the mass of the ball, we need to use the given information. We know the weight of the ball is equal to the vertical component of the tension force. We can calculate the vertical component of the tension force by multiplying the tension force by the sine of the angle between the string and the vertical (23 degrees).

Let's set up the equation:

Vertical component of tension force = Weight of the ball

Tension * sin(23) = mass * 9.8

We are given the length of the string as 35 cm. To convert it to meters, we divide by 100.

Now we can rearrange the equation to solve for the mass of the ball:

mass = (Tension * sin(23)) / 9.8

Since we are not given the tension in the string, we cannot directly calculate the mass of the ball using the information given. However, if you have additional information about the system, such as the tension in the string or the length of the string, you can substitute those values and calculate the mass using the equation above.