Capacitance and Capacitor
Parallel-plate capacitors, Dielectrics , Gauss's Law
Suitable for: AP Physics 2 (US), A-Level Physics (UK), IB Physics (Global), and Undergraduate Introductory Physics.
Key Ideas:
❖ Capacitance: The capacitance of a conductor is the amount of charge required to
increase its electric potential by one unit. Mathematically,
𝑄
𝐶=
𝑉
[Here, C = Capacitance, Q = Amount of Charge, V = Potential of the conductor]
❖ Capacitor: The mechanism used to store electric charge in a conductor is called a
capacitor.
❖ In the SI system, the unit of capacitance is the Farad (F).
❖ If 1C of charge is required to increase the electrical potential of a conductor by 1V,
then the capacitance of that conductor is 1F.
1𝜇𝐹 = 10−6 𝐹
1𝑝𝐹 = 10−12 𝐹
❖ The amount of charge per unit area is called the surface charge density.
❖ A dielectric is an electrical insulator that does not conduct electricity but can be
polarized by an applied electric field. For example, rubber, glass, wax, etc.
1
❖ Gauss’s Law: The total normal electric flux through any closed surface is 𝜀 times the
0
total charge enclosed by that surface.
Parallel-plate capacitor
A parallel plate capacitor consists of two closely spaced parallel metal
plates. One plate is insulated from the ground by means of insulating
support while the other plate is connected to the ground.
The figure alongside shows a parallel plate capacitor. When a charge of
+𝑞 is given to plate 𝑀, a charge of −𝑞 Is induced on plate 𝑁. Plate 𝑁 is
connected to the ground (Earth). The distance between the two plates is
taken to be 𝑑.
Calculation of the capacitance of a parallel-plate capacitor
Let,
The area of each of the two plates = A
The surface charge density on plate M = 𝜎
𝑞
∴ 𝜎=
𝐴
𝜎
The electric field between the plates, 𝐸 = 𝜀
0
[𝜀0 = 𝑇ℎ𝑒 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝑝𝑒𝑟𝑚𝑖𝑡𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑣𝑎𝑐𝑢𝑢𝑚]
Now,
Parallel-plate capacitors, Dielectrics , Gauss's Law
Suitable for: AP Physics 2 (US), A-Level Physics (UK), IB Physics (Global), and Undergraduate Introductory Physics.
Key Ideas:
❖ Capacitance: The capacitance of a conductor is the amount of charge required to
increase its electric potential by one unit. Mathematically,
𝑄
𝐶=
𝑉
[Here, C = Capacitance, Q = Amount of Charge, V = Potential of the conductor]
❖ Capacitor: The mechanism used to store electric charge in a conductor is called a
capacitor.
❖ In the SI system, the unit of capacitance is the Farad (F).
❖ If 1C of charge is required to increase the electrical potential of a conductor by 1V,
then the capacitance of that conductor is 1F.
1𝜇𝐹 = 10−6 𝐹
1𝑝𝐹 = 10−12 𝐹
❖ The amount of charge per unit area is called the surface charge density.
❖ A dielectric is an electrical insulator that does not conduct electricity but can be
polarized by an applied electric field. For example, rubber, glass, wax, etc.
1
❖ Gauss’s Law: The total normal electric flux through any closed surface is 𝜀 times the
0
total charge enclosed by that surface.
Parallel-plate capacitor
A parallel plate capacitor consists of two closely spaced parallel metal
plates. One plate is insulated from the ground by means of insulating
support while the other plate is connected to the ground.
The figure alongside shows a parallel plate capacitor. When a charge of
+𝑞 is given to plate 𝑀, a charge of −𝑞 Is induced on plate 𝑁. Plate 𝑁 is
connected to the ground (Earth). The distance between the two plates is
taken to be 𝑑.
Calculation of the capacitance of a parallel-plate capacitor
Let,
The area of each of the two plates = A
The surface charge density on plate M = 𝜎
𝑞
∴ 𝜎=
𝐴
𝜎
The electric field between the plates, 𝐸 = 𝜀
0
[𝜀0 = 𝑇ℎ𝑒 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝑝𝑒𝑟𝑚𝑖𝑡𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑣𝑎𝑐𝑢𝑢𝑚]
Now,
