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Unit E: Field and Potential

Equations

Type of field

Potential

Field strength

Force

Potential energy

Gravitational

V = Ep

M

 

Vg = - GM

r

g = -dV

dr

 

g = - GM

r2

F = mg

 

F = - GM1m2

r2

Ep = GM1m2

R

 

DEp = GM1m2 1 1

r1 r2

Uniform Electrical

V = Q

C

 

C = e0erA

d

E = V

D

 

E = s (charge density)

e0

F = qE

 

F = qV

d

Ep = qV

Non-uniform electrical

V = 1 Q

4pe0 r

E = F

q

 

E = 1 Q

4pe0 r2

F = 1 Q1q2

4pe0 r2

Ep = 1 Q1q2

4pe0 r

 

Uses

Escape Velocity

KE = mv2

Ep = GM1m2

r

mv2 = GM1m2

r

vesc = (2GM/r)

g = GM/r2

vesc = (2gr)

Unit H: Magnetic Fields and A.C.

Electric field

E = F = V

q d

 

Magnetic field

B = F

Il

 

Force on a moving charge

F = Bev

 

Hall voltage

-F = Bqv

-F = qE

-E = V

d

Bqv = qE = qV

d

V = Bvd

 

The Hall Voltage

Using Faraday's Law

Using F=Bev and F=qE

e = -dF

dt

-d = vt

e = -d(BA)

dt

e = -Bd(A)

dt

e = -Bd(length x distance)

dt

e = -Bd(lvt)

dt

Vh = Blv

-F = Bqv

-F = qE

-E=V

d

Bqv = qE

Bv = V

d

VH = Bvd

Measurement of e/m

-F = mv2

r

-F = Bev

-Energy = eV

-Energy = mv2

mv2 = eV

Bev = mv2

r

v = Ber

m

mv2 = eV

m (Ber/m) 2 = eV

m B2e2r2 = eV

m2

e = 2V_

m B2r2

 

Time period of a satellite

F = GMm/r2

F = mrw2

GMm/r2 = mrw2

GM/r3 = w2

w2 = (2p/T)2

GM/r3 = 4p2

T2

T = (4p2r3/GM)