What is the angle of the hanging ball in an electric field of 1.00×10^5 N/C?

In summary, the ball in the figure is in equilibrium with the tension force balancing the forces of gravity and the electric field. Using the equations E = F/q and F = mg, the values of Fx and Fy were calculated to be 2.5N and 0.1962N respectively. By finding the magnitude of the tension force using Ft = sqrt(Fx^2 + Fy^2), and using the equation tan(theta) = Fx/Fy, the angle theta was found to be 85.5126 degrees. However, there was a mistake in the calculation of the electric field due to incorrect unit conversion, resulting in an incorrect answer.
  • #1
Goldenwind
146
0

Homework Statement


http://session.masteringphysics.com/problemAsset/1001949/13/knight_Figure_25_69.jpg
An electric field 1.00×10^5 N/C causes the ball in the figure to hang at an angle. What is theta?



Homework Equations


E = F/q
F = mg

The Attempt at a Solution


The ball isn't accellerating, so it is in equilibrium. Sum of all forces is 0, so the tension force balences gravity + electric field.

E = F/q
F = Eq
F = 100000*(25*0.000001)
Fx = 2.5

F = mg
F = (0.002)(9.81)
Fy = 0.1962

Ft = Sqrt(Fx^2 + Fy^2)
Ft = 2.5076870697916038024546202698347

tan(theta) = Opp/Adj
tan(theta) = Fx/Fy
theta = arctan(2.5 / 0.1962)
theta = 85.5126 degrees

This answer is wrong.
Where is my mistake?
 
Last edited:
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  • #2
You have not given the unit for the electric field, but I'm assuming it's in SI.

> F = 100000*(25*0.000001)

The charge is in nC...
 
  • #3
Ah. Yeah, when I copied it over from the online problem, it didn't go.
E = 1x10^5 N/C
So I figured I'd convert q into the unit C, therefore get F in the unit N.
 
  • #4
Did you get the right answer?
 

FAQ: What is the angle of the hanging ball in an electric field of 1.00×10^5 N/C?

What is a hanging ball and how does it relate to electric fields?

A hanging ball is a small, lightweight object that is hung from a string or suspended in mid-air. It is often used in experiments to demonstrate the effects of electric fields. When a charged object is brought near the hanging ball, it will be attracted or repelled depending on the type of charge. This is because the electric field created by the charged object exerts a force on the hanging ball.

What is an electric field and how does it affect a hanging ball?

An electric field is a region in space where an electric force can be felt. It is created by charged objects and can exert a force on other charged objects within its vicinity. In the case of a hanging ball, the electric field created by a charged object will exert a force on the ball, causing it to move in the direction of the field.

What are the factors that affect the behavior of a hanging ball in an electric field?

The behavior of a hanging ball in an electric field is affected by several factors, including the strength of the electric field, the type and magnitude of charge on the hanging ball, the distance between the hanging ball and the charged object, and the mass of the hanging ball. These factors can all influence the magnitude and direction of the force exerted on the hanging ball.

How is the behavior of a hanging ball in an electric field related to the concept of electric potential energy?

The behavior of a hanging ball in an electric field is directly related to the concept of electric potential energy. When a charged object is brought near the hanging ball, it creates an electric field which exerts a force on the ball. This force causes the ball to move, and as it moves, it gains or loses electric potential energy depending on the direction of its movement. This concept is often used to explain the behavior of charged particles in electric fields.

What are some real-world applications of the concept of hanging ball and electric fields?

The concept of hanging ball and electric fields is used in various real-world applications such as electrostatic precipitators, which use electric fields to remove particles from industrial exhaust gases, and Van de Graaff generators, which use electric fields to generate high voltages. It is also essential in understanding the behavior of charged particles in devices like capacitors, electric motors, and particle accelerators.

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