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 r^2	F = mg F = - GM1m2 r^2	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 r^2	F = 1 Q1q2 4pe0 r^2	Ep = 1 Q1q2 4pe0 r

Uses

Escape Velocity

KE = ½ mv²

E_p = GM₁m₂

r

½ mv² = GM₁m₂

r

v_esc = Ö(2GM/r)

g = GM/r²

v_esc = Ö(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 = ½ mv²

½ mv² = eV

Bev = mv²

r

v = Ber

m

½ mv² = eV

½ m (Ber/m) ² = eV

½ 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 = Ö (4p²r³/GM)