Electrostatics and electric charge and field

[chiurox]

Homework Statement

A charged sphere is suspended by a nonconductive string in a uniform horizontal electric field. The electric field exerts a force on the sphere such that its equilibrium position is diplaced at an angle  = 30° relative to the vertical, as shown in the diagram below. The mass of the sphere is m = 4.0x10-3 kg, and the charge on the sphere is q = -3 uC.

a. What is the force on the sphere exerted by the electric charge?

b. What are the magnitude and the direction of the electric field?

c. The sphere is released from the string. What are the magnitude and the direction of the sphere's subsequent acceleration?

Homework Equations

F=k[(|q_1|q_2|)/r²]
E=F/q_o

The Attempt at a Solution

a)
I first tried to find the length of the displacement due to the force:
tan(theta)=F_E / F_mg
tan(30)=F_E / (9.8)(0.004)
F_E = 0.02 N is this correct?

b)
E=F/q_o
E=0.02 / -3
E=-0.0067 N/C correct?

c)I think the force would be the vertical component of the Electric Force (up) minus gravity, and the direction of the acceleration would be down (-). But how do I find the vertical component of the electrical force?

Thanks

 

[jandl]

If you do a sum of forces in the x and y directions and set them equal to zero you should have two equations (one for each direction) and two unknowns (the electric field strength and the tension in the string). This will give you the answers to both parts a and b.

Think about what happens when the sphere is released, how could you change the value of the tension in the equations to represent this?

 

[Moetasim]

for your question! I can provide some feedback and guidance on your attempt at solving this problem.

a) Your approach to finding the force exerted by the electric charge is correct. However, there are a few things to note. Firstly, it is important to use the correct units in your calculation. In this case, the mass should be in kilograms, not grams. So the calculation should be (9.8)(0.004) = 0.0392 N. Additionally, the angle theta should be in radians, not degrees. So the calculation should be tan(30*pi/180) = 0.5774. Finally, the force exerted by the electric charge should be in Newtons, not milliNewtons. So the final answer should be 0.02 N, as you correctly stated.

b) Your calculation for the electric field magnitude is correct. However, it is important to note that the charge on the sphere is negative, so the direction of the electric field should be towards the sphere, not away from it.

c) You are correct in your thinking that the force on the sphere will be the vertical component of the electric force (upwards) minus the force of gravity (downwards). To find the vertical component of the electric force, you can use trigonometry. The magnitude of the vertical component would be F_Esin(theta). So in this case, it would be (0.02)(sin(30*pi/180)) = 0.01 N. And as you mentioned, the direction of the acceleration would be downwards (-).

I hope this helps guide you in the right direction for solving this problem! Remember to always check your units and make sure they are consistent throughout your calculations. And don't hesitate to ask for clarification if you are unsure about anything. Good luck with your homework!