Topic A Flashcards
What is Coulomb’s law?
F =q1q2ˆr/4πε_0r^2
where ˆr is the unit vector along the line connecting the two charges, and ε_0 is the permittivity of free space
The force between two point charges q1 and q2 is proportional
to the inverse square of the distance r between them
Equation for electric field due to a test charge?
If a test charge Qt, placed at some
position in space, experiences an electric force F, then the E-field at that point is given by
E=limF/Q_T
where the limit Qt–>0 is required so that Qt does not perturb the charges which produce F
and E.
(NC^-1 or Vm^-1)
What is the equation for electrostatic force?
The electrostatic force, F, which acts on a charge, q, placed in an electric field, E, is then given
by
F=qE
Electric due to point charge equation?
E =qr^/4πε_0r^2
Electric field due to more than one charge?
Using principle of superposition can be applied to find the total E-field at a given point.
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The electric field for continuous charge distribution?
To determine the total field due to the distributed charge:
E = ∫dqˆr/4πε_0r^2
the integral it is necessary to express dq in terms of r
Use charge density
3D dq = ρ dV dV = element of volume
2D surface dq = σ dA dA = element of area
1D line dq = λ dℓ dℓ = element of length
Electric field lines?
The tangent to the lines at any point gives the direction of the E-field at that point.
- Lines start on positive charges and terminate on negative ones.
- The density of lines gives an indication of the field strength at a given point.
What is Gauss’ Law (Integral Form)?
Φ = ∫E⋅dS = ΣQ1/ε_0
‘the outward flux of E over any closed surface S (no edges) is equal to the algebraic sum of the charges
enclosed by the surface S divided by ε_0.’
Finding the E-field
resulting from systems with high degree of symmetry?
- Decide shape of Gaussian surface
- What is the form of electric field
- Find the flux through the gaussian surface (all points perpendicular so E xS)
- Charge enclosed in gaussian surface
- Use Gauss’s law
Flat infinite sheet, line charge or spheres are examples
What happens to electric fields in conductors?
In a conductor, charges are free to move in an
electric field
The displaced charges produce an induced field Eint.
Charges will move until Eint exactly balances Eext.
There is then no net field inside the conductor.
By Gauss’ law,any excess charge must be on the surface of the conductor.
so E=0
Change in potential energy equation?
ΔU=∫-q1q2dr/4πε_0r^2=q1q2/4πε_0(1/r_2-1/r_1)
As the electric force is a radial or central one, work is only done for movement along the line
joining the two charges. It is path independent
Potential energy is always relative, there is no absolute zero
define the potential energy as being zero when the charges are an infinite distance apart
U=q1q2/4πε_0r
What is the potential energy of a collection of N>2 charges?
U=Q1Q2/(4πε_0r12)+ Q2Q3/(4πε_0r23)+ Q3Q1/(4πε_0r13)
What is the potential energy of tow charges assuming zero value for infite speration?
U = Q1Q2/(4πε_0r)
What is the electric potential?
V_BA = LimO_BA/Q_t
What is the electric potential from a series of point charges?
N (i=1)ΣQ_i/4πε_0r_i)
