Sections 7-10 Flashcards
What is the equation for potential energy associated with the coulomb interaction of two charges?
(q1q2)/(4πϵ0*r)
What is the equation for potential energy of a point charge at a point in space?
q/(4πϵ0(r-r’))
How do you derive the integral for potentials?
Vab = Va-Vb = Wab / q0
Wab = Integral from a to b of F.dl, and F = q0*E
Rearrange and gives you the integral
How do you calculate a potential?
You find the integral between infinity and a point a within the electric field of E*dl, where E is the electric field and l is the distance it moves.
How do you explicitly calculate a path integral?
You find the unit vector associated with the vector quantities and (hopefully) they will cancel out leaving just the quantities magnitudes. You can then take the constants out and work out the integral.
How do you calculate the potential of an infinite line of charge?
Need the equation for the electric field of an infinite line of charge. Use this in the potential integral and pick a reference point for the end point.
How do you use the method of image charges to work out the surface charge density of a conductor?
Place an image charge opposite the charge and work out the electric field using the electric field equation for each charge. Electric field inside the conductor is zero, so there must be a surface charge.
How do you calculate potential gradients?
-vV = -dV/dx i - dV/dy j - dV/dz k = E where V is the potential,v is the gradient and E is the electric field.
What is the equation for capacitance?
C = Q/V, where Q is the charge and V is the potential difference between the plates.
What is the equation for capacitance of two parallel plates? How do you derive this?
C = ϵ0*A/d Electric field between the plates is -σ/ϵ0, where σ is the surface charge density (Q/A). Thus, E = Q/(ϵ0*A). For uniform potential difference, V = Ed, so V = (Q*d)/(ϵ0*A). Rearrange for capacitance.
How do you derive the capacitance of a cylindrical capacitor?
Use the potential of an infinite line of charge and set the two radii to the radii of the inner and outer cylinder. Then use lambda = Q/L
How do you derive the capacitance of a spherical capacitor?
Use the potential of a sphere centered on a charge q but change 1/r for 1/r2 - 1/r1, where r2 and r1 are the radii of the respective spheres. Then use the charge stored on each sphere as q = σ4πr^2, where σ is the surface charge density.
What is the self-capacitance of a single spherical plate of radius r?
C = 4πϵ0r
How do you add the capacitance of capacitors in series/parallel?
Series: 1/C = 1/C1 + 1/C2 + … Parallel: C = C1 + C2 + …
What are the 3 main equations for energy stored in a capacitor?
1/2 * Q/V 1/2 * C*V^2 1/2 * Q^2/C
