11.1 Basic Concepts and Formulae
461
V =
q
8πε 0 R
3 −
r 2
R 2
(r ≤ R)
(11.13)
=
q
4πε 0 r
(r ≥ R)
(11.14)
Calculation of E from V
E = −
dV
dr
(11.15)
Surface charge density
σ =
q
4πr 2
(11.16)
Electric potential energy (U )
U =
1
4πε 0
q 1 q 2
r
(11.17)
Capacitors
C =
q
V
(11.18)
where C is the capacitance.
Capacitance of a sphere
C =
q
V
= 4πε 0 R
(11.19)
The parallel plate capacitor
C =
ε 0 KA
d
(11.20)
where A is the area of each plate, d is the distance of plates and K is the dielectric
constant.
Equilibrium of an Oil Drop
Let a charge −q be acquired by a small oil drop placed between two charged plates,
the upper one being positively charged. The drop is under the joint action of two
forces, the electric force acting upwards and the gravitational force acting downwards. If the drop is to remain suspended, then the condition for equilibrium is
q E = mg
(11.21)
461
V =
q
8πε 0 R
3 −
r 2
R 2
(r ≤ R)
(11.13)
=
q
4πε 0 r
(r ≥ R)
(11.14)
Calculation of E from V
E = −
dV
dr
(11.15)
Surface charge density
σ =
q
4πr 2
(11.16)
Electric potential energy (U )
U =
1
4πε 0
q 1 q 2
r
(11.17)
Capacitors
C =
q
V
(11.18)
where C is the capacitance.
Capacitance of a sphere
C =
q
V
= 4πε 0 R
(11.19)
The parallel plate capacitor
C =
ε 0 KA
d
(11.20)
where A is the area of each plate, d is the distance of plates and K is the dielectric
constant.
Equilibrium of an Oil Drop
Let a charge −q be acquired by a small oil drop placed between two charged plates,
the upper one being positively charged. The drop is under the joint action of two
forces, the electric force acting upwards and the gravitational force acting downwards. If the drop is to remain suspended, then the condition for equilibrium is
q E = mg
(11.21)