Analogy between Electrostatics and Gravitation
Electrostatics Gravitation
1 Kq1q2 Gm1m2
1) q, 4πε , F = 1) m, G, F =
0 r2 r2
2) Attraction & Repulsion 2) Only Attraction
F U F
3) F ; E = q ; U, V = 3) Fg , Eg = = g ; Ug ; V
q m
4) F = qE & U = qV 4) F = mE & U = mV
Kq1q2 Kq Gm1m2
5) U = &V = 5) U = − &V =
r r r
6) Induction, dipole 6) No Induction & No dip
7) Effect of medium is there 7) No effect of medium.
, Analogy between Electrostatics and Gravitation
Gauss’s Law in Electrostatics Gauss’s Law in Gravitatio
qin
ϕ = රE. dԦs = ϕ = රEg. ds = −4πG menc
ε0
(1) Point Charge Point Mass
𝐤𝐐 𝐤𝐐 𝐆𝐌 −
𝐄= 𝟐 , 𝐕= 𝐠= 𝟐 , 𝐕𝐆 =
𝐫 𝐫 𝐫
(2) Uniform charged ring Ring of uniform mass dis
𝐤𝐐𝐱 𝐆𝐌𝐱
(a) 𝐄 = 𝟑Τ 𝟐 𝐨𝐧 𝐚𝐱𝐢𝐬 𝐠= 𝟑 Τ𝟐 𝐨𝐧 𝐚𝐱𝐢𝐬
𝐫 𝟐 +𝐱 𝟐 𝐫 𝟐 +𝐱 𝟐
𝐫 𝐫
E is max. when x = g is max. when x =
𝟐 𝟐
𝐤𝐐 𝐤𝐐 −𝐆𝐌 −𝐆𝐌
(b) 𝐕 = on axis, 𝐕𝐆 = on axis, 𝐫 at
𝐫 𝟐 +𝐱 𝟐 𝐫 𝐫 𝟐 +𝐱𝟐
at center
Electrostatics Gravitation
1 Kq1q2 Gm1m2
1) q, 4πε , F = 1) m, G, F =
0 r2 r2
2) Attraction & Repulsion 2) Only Attraction
F U F
3) F ; E = q ; U, V = 3) Fg , Eg = = g ; Ug ; V
q m
4) F = qE & U = qV 4) F = mE & U = mV
Kq1q2 Kq Gm1m2
5) U = &V = 5) U = − &V =
r r r
6) Induction, dipole 6) No Induction & No dip
7) Effect of medium is there 7) No effect of medium.
, Analogy between Electrostatics and Gravitation
Gauss’s Law in Electrostatics Gauss’s Law in Gravitatio
qin
ϕ = රE. dԦs = ϕ = රEg. ds = −4πG menc
ε0
(1) Point Charge Point Mass
𝐤𝐐 𝐤𝐐 𝐆𝐌 −
𝐄= 𝟐 , 𝐕= 𝐠= 𝟐 , 𝐕𝐆 =
𝐫 𝐫 𝐫
(2) Uniform charged ring Ring of uniform mass dis
𝐤𝐐𝐱 𝐆𝐌𝐱
(a) 𝐄 = 𝟑Τ 𝟐 𝐨𝐧 𝐚𝐱𝐢𝐬 𝐠= 𝟑 Τ𝟐 𝐨𝐧 𝐚𝐱𝐢𝐬
𝐫 𝟐 +𝐱 𝟐 𝐫 𝟐 +𝐱 𝟐
𝐫 𝐫
E is max. when x = g is max. when x =
𝟐 𝟐
𝐤𝐐 𝐤𝐐 −𝐆𝐌 −𝐆𝐌
(b) 𝐕 = on axis, 𝐕𝐆 = on axis, 𝐫 at
𝐫 𝟐 +𝐱 𝟐 𝐫 𝐫 𝟐 +𝐱𝟐
at center
