Voltage dealing with two parallel plates

[Giuseppe]

Hey guys. I'm having trouble analyzing a part of this problem.

Two conducting, infinite sheets of charge (with thickness a) are fixed perpendicular to the x-axis as shown. The sheet from x = -2a cm to x = -a has a net charge per unit area -s and the sheet from x = +a to x = +2a has a net charge per unit area +s. (Note: the notation Vx1 » x2 is equivalent to Vx2 - Vx1.)

So basically the left plate is situated at -2a to -a, and the right play is situated at a to 2a. I know the electric field flows to the left.

Knowing this I must answer these questions.

1. the potential going from the right side of the right plate and approaching the plate is...
a. <0
b. =0
c. >0

I believe that it is zero because there isn't a net electric field at this point. Is that right?

2. The potential going from the edge of the right plate through the right plate to the other side is...
a.>0
b.=0
c.<0
I want to say its >0, but I don't know exactly why. Can anyone lead me in the right direction here?

3. The potential going from the inside of the right plate to the inside of the left plate is...
a.>0
b.=0
c.<0
I say it is <0 because the electric field is uniform on the inside. Also, since you are moving to the negative end of the field, potential is negative.

Any help is appreciated. Thanks!

 

[Astronuc]

By +s and -s, does one mean +$\sigma$ and -$\sigma$, which means the plate on the right (+x) has a positive charge and the plate on the left (-x) has a negative charge. Therefore the plate on the right has a higher potential than the plate on the left.

The electric field points for + potential (+ charge) to - potential (- charge), by convention.

Somewhere in between the potential must be zero, but the electric field is not zero anywhere between the plates. Think of a parallel plate capacitor.

 

[quicknote]

As a scientist, the first thing I would recommend is to review the concept of voltage and how it relates to electric fields and potential energy. Voltage is a measure of the potential difference between two points in an electric field. In this case, the two parallel plates are creating an electric field between them, and the voltage will vary at different points within that field.

1. The potential going from the right side of the right plate and approaching the plate is...
a. <0 b. =0 c. >0

Since the right plate has a positive charge, the electric field will point away from the plate, meaning that the potential decreases as you move away from the plate. Therefore, the potential at the right side of the right plate and approaching the plate will be <0.

2. The potential going from the edge of the right plate through the right plate to the other side is... a.>0 b.=0 c.<0

As mentioned before, the electric field points away from the right plate. When you move through the plate, you are moving in the opposite direction of the electric field, meaning that the potential will increase. Therefore, the potential going from the edge of the right plate through the right plate to the other side will be >0.

3. The potential going from the inside of the right plate to the inside of the left plate is... a.>0 b.=0 c.<0

Since the electric field is uniform on the inside of the plates, the potential will remain constant as you move from one plate to the other. However, since the electric field is pointing from the right plate to the left plate, the potential will decrease as you move in that direction. Therefore, the potential going from the inside of the right plate to the inside of the left plate will be <0.

I hope this helps clarify the concept of voltage in relation to two parallel plates and their electric field. It's important to remember that voltage is a measure of potential difference and can vary at different points within an electric field. Keep reviewing the concept and practicing problems to solidify your understanding. Good luck!