Electric Field at Surface of Earthed Sphere (using image charges)

In summary, when a charged sphere is a distance d from the centre of an earthed conducting sphere, an image charge (q') can be located at a distance b from the centre of the sphere, with q'= -(aq/d) and b=(a^2)/d. The electric field at point p, located on the surface of the sphere directly above the surface, is non-zero due to the non-zero electric potential everywhere except on the surface and in the interior. This is similar to how a gravitational field can exist even when the potential is zero on the surface.
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"A charged sphere is a distance d from the centre of an earthed sphere conducting sphere of radius a. An image charge (q') for this system is located at a distance b from the centre of the sphere where:

q'= -(aq/d) and b=(a^2)/d

Calculate the expression for the Electric field at point p being on the surface of the sphere directly above the surface."

Would the Electric field be zero. As the Electric potential would surely be zero on the surface of the sphere and the E field is just -grad of the potential?
 
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The potential is zero on the surface (and in the interior), but non-zero everywhere else. This gives a non-zero electric field.
In a similar way, you can define the floor as area of zero gravitational potential - and still get a gravitational field.
 

FAQ: Electric Field at Surface of Earthed Sphere (using image charges)

What is the concept of image charges in relation to electric field at the surface of an earthed sphere?

The concept of image charges involves using a hypothetical charge, called an image charge, to mimic the behavior of the actual charge in a system. In the case of an earthed sphere, the image charge is placed at a specific distance from the surface of the sphere to help calculate the electric field at the surface.

How does the presence of an earthed sphere affect the electric field around it?

An earthed sphere acts as a conductor, meaning it can easily conduct electricity. This causes the electric field lines to terminate on the surface of the sphere, creating a uniform electric field in the surrounding space. This also means that the electric field inside the sphere is zero.

What is the equation for calculating the electric field at the surface of an earthed sphere using image charges?

The equation is given by E = (1/4πε0) * (q/R2 + qi/d2), where E is the electric field, q is the actual charge, R is the radius of the earthed sphere, qi is the image charge, and d is the distance between the charge and the image charge.

Can image charges be used to calculate the electric field at any point in space?

No, image charges can only be used in certain special cases, such as when dealing with conductors or when the system has a high degree of symmetry. In other cases, more complex methods may be needed to calculate the electric field.

How does the distance between the actual charge and the image charge affect the electric field at the surface of an earthed sphere?

The distance between the actual charge and the image charge, represented by d in the equation, has an inverse squared relationship with the electric field. This means that as the distance increases, the electric field decreases. This is why the image charge is typically placed at a specific distance from the surface of the earthed sphere to achieve a certain electric field at the surface.

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