Fields Flashcards
Direction of the field
Gravitational- direction of the force on a small test mass at that point
Electric- direction of a force on a positive charge at that point
Magnetic- direction of force in a magnetic North Pole
Radial field
Directed towards centre
Diverges
Strength of field decreases as density of lines decreases
Uniform field
Lines are equally spaced and parallel
Same magnitude and direction throughout
Near field limit
Newton’s law of gravitation
F= GMm/ r^2
Gravitational constant
6.67 x 10^-11 Nm^2kg^-2
Relationship T and r
Kepler’s law
T^2 proportional to r^3
T^2 = 4pi^2/ GM r^3
As r increases …
Speed of satellite decreases (v = GM/r)
Period of satellite increases
Geosynchronous orbit
Period of 24 hours
Or it’s above the equator
Or it’s in the same direction as the Earth’s rotation
Geosynchronous satellites in communication
Dish can be pointed at a fixed point (does not have to track)
Dishes needed as the weak signal can be collected across the area of the disc and focussed on the receiving antenna
Gravitational field strength
g = GM/r^2
Gravitational potential
V =-GM/r
Scalar
Units = J/kg
V at infinity
0
Work (gravitational)
W = mdV
Away = positive
Towards =negative
Gravitational potential energy
U= -GMm/r
Kinetic energy
Ek= GMm/2r
Total energy (gravitational)
Et = -GMm/2r
Negative
Increasing Et
Gains energy, less negative, r increases
Escape velocity
Root (2gR)
Coulomb’s law
F = Qq/4pi epsilon r^2
Positive
Repulsive
Epsilon 0
Permittivity of free space
Ease of setting up an electric field
8.85 x10^-12
Similarities between gravitational and electric fields
Inverse square law for forces
Non contact forces
Infinite range
Difference gravitational and electric fields
Electric acts on changes, gravitational on masses
Gravitational is attractive whereas electric can be attractive or repulsive
Electric field strength
E= Q/ 4 pi epsilon r^2
Electric potential
V = Q/ 4pi epsilon r
Scalar
Sign of W
+/- negative work
+/+ or -/- positive work
Potential gradient (electric)
E = dV/ dr
Work (electric)
W =qdV
Equipotential lines
Lines of equal potential
At right angles to the field
Electrical potential energy
U = Qq/4 pi epsilon r
Energy of whole system
Distance of closest approach
R min = Qq/ 2pi epsilon m v^2
Capacitance
C=Q/V
Farads F
Work done by a capacitor
E = 1/2 QV
E = 1/2 C V^2
E = 1/2Q^2/C
Time constant
RC
Seconds
Charging a capacitor
Charge
Q = Qmax (1-e^-t/RC)
Charging a capacitor
Voltage
V = Vmax (1-e^-t/RC)
Charging a capacitor
Current
I = Imax e^-t/RC
Discharging a capacitor
Charge
Q = Qo e^-t/RC
Discharging a capacitor
Voltage
V = Vo e^-t/RC
Discharging a capacitor
Current
I = Io e^-t/RC
Relative permittivity
Epsilon r = C/Co
C = capacitance with dielectric Co = capacitance with vacuum
Capacitance equation (dielectric)
C = epsilon o epsilon r A/ d
Current at right angles to the field feels force
F = BIl
Fleming’s left hand rule
Thumb= force 1st = field 2nd = current
Force on a moving charge perpendicular to the field
F = Bqv
Charged particle moving parallel to a magnetic field
No force
Radius of a circular path
r= mv/Bq
Time period for 1 full circle
T = 2 pi m/ Bq
Acceleration in a magnetic field
Changes direction so changes v so accelerated
Circular path
F is perpendicular to v and B
No work done so Ek does not change, so no increase in speed
Why a cyclotron needs to be evacuated
Collisions, loss of Ek, deceleration, changes v which changes r
Alternating charge of the dees of a cyclotron
So proton accelerated across the gap
Needs to alternate and reverse electric field
Polarity can switch at regular intervals
Frequency = Bq/ 2 pi m
The feature of the ions that allows them to be separated
In ion separator v B and q are constant
r= mv/Bq
Ions departed due to their mass
Velocity selected in a velocity separator
Only 1 velocity where Bqv= Eq and there will be no deflection
V=E/B
Why ions originally have a range of speeds
Gases
Random continuous motion of gases
Brownian motion
Move with varying speeds and directions
Magnetic flux
Phi= BA cos theta
Theta= angle between field lines and normal to plane of the area
How to reduce magnetic flux
Reduce B
Reduce A
Rotate- as the angle changes as will the area perpendicular to the field
Faraday’s law induced EMF
EMF = N dphi/ dt
To increase the induced EMF
Increase N
Increase v and increase l (which increases A)
Increase B
For a rod length l moving at constant speed v
EMF = BvL
