What is the magnitude of the electric field?

[las90]

Homework Statement

What is the magnitude of the electric field in the region between the plates?
The charge on the sphere is 5.00 mC
The image needed to visualize situation:
http://www.webassign.net/userimages/66097?db=v4net
mass of sphere = 3.2grams

Homework Equations

F = EQ
Fg = mg

The Attempt at a Solution

First, I drew a free body diagram. Tension went up along the thread, Fg (gravity) was pointing down at the electrical force was pointing to the right. I then solved for Fg, which I got .03136N from multiplying (9.8)(.0032). I then set Ft(tension) * cos30 = .03136, which I then got Ft = .0362114089. I then plugged my Ft, multiplied it by sin30 in order to get the electrical force, which turned out to be .0181057044. From there, I used the equation F=EQ, which I did (.0181057044)(5e-3), which i then ended up with 3.621140888 N/C which was obviously the wrong answer.

 

[anathema]

Hello there,

Thank you for your post. In order to calculate the magnitude of the electric field in the region between the plates, we need to use the equation E = F/q, where E is the electric field, F is the force, and q is the charge.

In this scenario, we have a charge of 5.00 mC (5e-3 C) and a force of 0.0181057044 N. Plugging these values into the equation, we get:

E = 0.0181057044 N / 5e-3 C = 3.621140888 N/C

So, your calculation was correct. The issue may be with the units - make sure to double check and use consistent units throughout your calculations. Also, it is important to note that the direction of the electric field is from positive to negative charges, so in this case, the electric field would be pointing from the positively charged sphere towards the negatively charged plate.

I hope this helps. Keep up the good work in your studies!

 

[nlightner]

The magnitude of the electric field in the region between the plates can be found by using the equation F=EQ, where F is the force exerted on the sphere, E is the electric field, and Q is the charge on the sphere. In this case, the charge on the sphere is given as 5.00 mC. However, in order to calculate the force on the sphere, we need to consider all the forces acting on it. These include the force of gravity (Fg) and the tension in the thread (Ft).

To find the tension in the thread, we can use the equation Ft*cos30 = Fg, where Ft is the tension and cos30 is the cosine of the angle between the thread and the horizontal. From this, we can solve for Ft and get a value of 0.0362114089 N.

Now, to find the electrical force, we need to use the equation Ft*sin30 = EQ, where sin30 is the sine of the angle between the thread and the horizontal. From this, we can solve for E and get a value of 3.621140888 N/C. This is the magnitude of the electric field in the region between the plates.

It is important to note that in this scenario, the mass of the sphere does not affect the magnitude of the electric field. The only factors that affect the electric field are the charge on the sphere and the distance between the plates.