Question
(i) If two similar large plates, each of area A having surface charge densities 1s and 2s are separated by a distance d in air, find the expressions for
(a) field at points between the two plates and on outer side of the plates. Specify the direction of the field in each case.
(b) the potential difference between the plates.
(c) the capacitance of the capacitor so formed.
(ii) Two metallic spheres of radii R and 2R are charged so that both of these have same surface charge density s. If they are connected to each other with a conducting wire, in which direction will the charge flow and why ?
Solution
i)
Given, each plate has an area A and surface charge densities 1s and 2s respectively.
The plates 1 and 2 be separated by a small distance d.
For plate 1:
Surface charge density,
For plate 2:
Surface charge density,
Electric field in different regions:
Outside region 1,
E =
Outside region 2,
Inner region:
In the inner region between plates 1 and 2, electric fields due to the two charged plates add up.
That is,
Direction of electric field is from positive to the negative plate.
b) Potential difference between the plates, V = Ed =
c) Capacitance of the capacitor so formed, C =
ii) Potential on and inside of charged sphere is given by,
That is, the sphere having larger radius will be at a higher potential.
Therefore, charge will flow from bigger sphere to smaller sphere.
Given, each plate has an area A and surface charge densities 1s and 2s respectively.
The plates 1 and 2 be separated by a small distance d.
For plate 1:
Surface charge density,
For plate 2:
Surface charge density,
Electric field in different regions:
Outside region 1,
E =
Outside region 2,
Inner region:
In the inner region between plates 1 and 2, electric fields due to the two charged plates add up.
That is,
Direction of electric field is from positive to the negative plate.
b) Potential difference between the plates, V = Ed =
c) Capacitance of the capacitor so formed, C =
ii) Potential on and inside of charged sphere is given by,
That is, the sphere having larger radius will be at a higher potential.
Therefore, charge will flow from bigger sphere to smaller sphere.
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