If potential (in volts) in a region is expressed as , the electric field (in N/C) at point is:
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Potential in a region
As we know the relation between electric potential and electric field is
A capacitor of is charged as shown in the diagram. When the switch is turned to position 2 , the percentage of its stored energy dissipated is :
A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge (having a charge equal to the sum of the charges on the 4 and capacitors), at a point distance from it, would equal:
Charge on is
The voltage across is
Voltage across is also
Charge on capacitor
Total charge on and
(i)
(ii)
(iii)
(iv)
A positive charge, is moved from to in each diagram.
In all the four cases the work done is the same
Minimum work is required to move in figure (i)
Maximum work is required to move in figure (ii)
Maximum work is required to move in figure (iii)
As the regions are of equipotentials, so Work done
is same in all the cases hence work - done will also be same in all the cases.
A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system
decreases by a factor of 2
remains the same
increases by a factor of 2
increases by a factor of 4
The electrostatic force between the metal plates of an isolated parallel plate capacitor having a charge and area A, is
independent of the distance between the plates
linearly proportional to the distance between the plates
inversely proportional to the distance between the plates
proportional to the square root of the distance between the plates
Electrostatic force between the metal plates
For isolated capacitor constant
Clearly, is independent of the distance between plates.
A short electric dipole has a dipole moment of . The electric potential due to the dipole at a point at a distance of from the centre of the dipole, situated on a line making an angle of with the dipole axis is :
.
zero
Given,
Dipole moment of short electric dipole,
Distance from centre of dipole,
Electric potential,
The capacitance of a parallel plate capacitor with air as medium is . With the introduction of a dielectric medium, the capacitance becomes . The permittivity of the medium is :
Capacitance of a parallel plate capacitor with air is
Here, area of plates of capacitor,
distance between the plates
Capacitance of a same parallel plate capacitor with introduction of dielectric medium of dielectric constant is
Dividing (ii) by (i)
In a certain region of space with volume , the electric potential is found to be throughout. The magnitude of electric field in this region is :
Since, electric potential is constant throughout the volume, hence electric field, .
A parallel plate capacitor has a uniform electric field ' ' in the space between the plates. If the distance between the plates is ' ' and the area of each plate is ' ', the energy stored in the capacitor is ( permittivity of free space)
Energy density i.e. with electric field
Energy stored in the capacitor
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