A uniformly charged ball of radius a and charge -Q is at the center of a hollow metal shell with…
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Question “A uniformly charged ball of radius a and charge -Q is at the center of a hollow metal shell with…”
A uniformly charged ball of radius a and charge -Q is at the center of a hollow metal shell with inner radius b and outer radius c. The hollow sphere has a netcharge of +2Q a. determine the the electric field strength in the four regions r_<a, a<r, b_<r_<c, and r>c b. draw a graph of E versus r from r=0 to r=2c
Answer
Gauss’s law, which links the electric flux through a material to the charge contained within it, can be used to determine the electric field at different locations due to a system that consists of a uniformly charged ball enclosed by a hollow metal shell.
The Gauss law can be described as,
refers to the charge contained within the surface.
represents the flux through it.
The electric flux can be described as:
Combining both equates, rearrange E.
The concept of sphericalsymmetry of charge distribution states that the direction of the electric field will be either radially inwards or outwards.
Select Gaussian surface at
, where the charge is negatively so that the direction of the electric field is inward.
From Gauss’s law
refers to the volume charge density for the charged metal ball.
This table shows the relationship between volume charge density and volume.
Now, we will choose the Gaussian surface to the region
, and on applying Gauss law to this region, we get,
The electric field at
therefore is
.
The Gaussian surface can be found in the
region. By applying Gauss law to the region, we obtain:
The net field within the metal shell is therefore zero because there is no charge in the conductor/metal, so the flux through the Gaussian surface here is also zero.
The electric field at
has been replaced by
.
Let’s choose the Gaussian surface for the region of
. If we apply Gauss law to the region, then,
The shell’s net cost is
The region of
has an electric field strength.
In vector notation
The electric field at
has been replaced by
.
Conclusion
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