# Magnitude of electric field between two concentric oppositely charged

• sa1988
In summary, the electric field between two concentric oppositely charged spheres is E=Q/(4πεab). E=Q/4πεr2 is the correct answer.
sa1988

## Homework Statement

Magnitude of electric field between two concentric oppositely charged spheres.

## The Attempt at a Solution

So I first went with the simple electric field equation E=V/d

So I have the potential difference V between the two sphere surfaces. I can't do Latex but hyperphysics has it anyway:

So I know V.
And surely, in E=V/d, the distance d is simply b-a.

So finally I sub my V and d into the equation and I'm left with:

E = Q/(4πεab)

Which looks reasonable enough.. But all sources on the Internet tell me that the answer is simply:

E=Q/4πεr2

The real confusing thing for me here is... What is 'r' ? What is it the radius from? The radius from the centre? Or from the surface of the inner sphere? Or something else..??

I fear my problem may be with the fact that I used E=V/d, which is possibly only valid for charged plates, rather than spheres? Either way, I'm still a little confused about what the 'r' actually means in the correct answer.

Thanks for any guidance :thumbs:

Should 'r' be defined such that:

a < r < b

?

The expression above the ##\Delta V## formula you show is that selfsame E=Q/(4πεr2) !
Read up on Gauss's theorem (ibidem, another two lines higher up, or Gauss's law)

Your E=V/d is a special case for a constant ##\vec E ## all over the place.
Otherwise (here for instance) ##\vec E = -\vec\nabla V##.

And r is simply the distance to the center.

Oh dear oh dear! So yeah I guess my main error was for the E=Vd part.

I've been taught about E = -∇V before, and yeah that makes perfect sense come to think of it.

Electric/Magnetic fields is certainly my weakest subject at the moment. Must study harder!

Thanks for showing me that :thumbs:

I would like to clarify that the equation E=V/d is only applicable for charged plates, as you have correctly mentioned. In the case of concentric spheres, the electric field between them is not constant and it varies with distance from the center. This is because the electric field lines are radial and the distance from the center to a point on the field line changes as we move along the field line.

Now, coming to the correct equation, E=Q/(4πεr^2), where r is the distance from the center, is known as Coulomb's law. It is the fundamental law that describes the relationship between the magnitude of electric charge, Q, and the distance, r, between the charges. In this case, r is the distance from the center of the spheres, as the electric field is radial.

I hope this clarifies your confusion. It is always important to understand the underlying principles and equations before using them in calculations. Keep up the good work!

## 1. What is the formula for calculating the magnitude of electric field between two concentric oppositely charged objects?

The formula for calculating the magnitude of electric field between two concentric oppositely charged objects is E = kQ/r2, where E is the electric field, k is the Coulomb's constant (9 x 109 Nm2/C2), Q is the magnitude of charge on one of the objects, and r is the distance between the two objects.

## 2. How does the magnitude of charge affect the electric field between two concentric oppositely charged objects?

The magnitude of charge on the objects directly affects the electric field between them. As the magnitude of charge increases, the electric field also increases. This means that the force between the two objects becomes stronger.

## 3. What is the direction of the electric field between two concentric oppositely charged objects?

The direction of the electric field is always from positive to negative charge. This means that the electric field lines will point away from the positively charged object and towards the negatively charged object.

## 4. How does the distance between two concentric oppositely charged objects affect the magnitude of electric field?

The magnitude of electric field between two concentric oppositely charged objects is inversely proportional to the square of the distance between them. This means that as the distance increases, the electric field decreases and vice versa.

## 5. Is the magnitude of electric field between two concentric oppositely charged objects affected by the medium between them?

Yes, the magnitude of electric field is affected by the medium between two concentric oppositely charged objects. The medium can either enhance or decrease the electric field depending on its properties, such as its dielectric constant and conductivity.

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