Electrostatics III Pt II

Calculating the Electric Potential 
Knowing the potential energy, we can calculate the electric potential of a charge q at a point using what equation?

The parallel-plate capacitor creates a uniform electric field (state the formula) 
The plates have area A and separation d. Let U_e = 0 when a mobile charge q is at the negative plate (x = ___). The charge's potential energy at any other position x is then the amount of work necessary to move the charge from the ______ ______ to that position 
The hand does work on q to move it ______ against the field, thus giving the charge electric potential energy

The hand push the charge q towards the positive plate at a constant speed. Thus, F_hand = ____ = ____
State the formula for the work to move the charge to position x: 
W (2)
State the formula for the work to move the mobile charge to position x within the contex of potential energy: 
W (2)

The electric potential of the parallel-plate capacitor at position x, measured from the negative plate (U_e = ___, V = ___), is: 
State the formula for V (3)
The electric potential increases linearly from the ______ plate (x =  ___) to the ______ plate at (x = ___)
The potential difference ΔV_c between the two capacitor plates is: 
ΔV_c = _______ = _____

A 2-D equipotential map is represented below. The green dashed lines are _________ lines or simply _________.

To find the electric potential due to a single fixed charge q, we first find the electric potential energy when a second charge q' is a distance r_B away from q
ΔU_e = ______
Take (U_e)_A = 0 to be at a point infinitely far from q (i.e. r_A → ∞) for convenience. This is a good reference point as the influence of the point charge q goes to _____ as we get _____ far from the charge 

The force on q' gets larger as it approaches q. Thus, work done is not by a constant force and cannot use the equation W = Fd to find the work for a ______ ______ q'

An exact calculation finds the electric potential energy of two point charges separated by distance r is: 
U_e = ______
In the case where q and q' are opposite charges, the potential energy of the charges is _______. q' _______ toward fixed charge q. U_elec = 0 when q' is ______ far from q. As q' approaches q it gains ______ energy and loses ______ energy
The y-axis is U_elec

For a charge q' that is a distance r from a charge q, the electric potential is related to the potential energy by V = ____. 
The electric potential at distance r from a point charge q is: 
V = ____ = ____ = ____
Only the source charge appears in this expression. (The source charge creates the _______ _______ around it)

Electric potential at distance r from a point charge q
Restate the formulas for V(3)

The electric potential at a distance r > R from the center of a sphere of radius R and with charge Q is the same as the _____ _____ at a distance r from a point charge.

The potential V₀ is the potential at the surface of the charged sphere
V₀ = _____ = _____
The charge for a sphere of radius R is therefore: 
Q = _____
The potential outside a charged sphere: 
V = ______ = _______ = _____
The potential ______ _____ with distance from the center

V is constant everywhere on the surface of a charged conductor in equilibrium. ΔV = ___ between any two points on the surface. No work is required to move a _____ _____ between any two points on the surface. The surface of any charged conductor in electrostatic equilibrium is an ________ ______. Why is it that the electric potential is constant everywhere inside the conductor and equal to the value at the surface.

Consider a solid metal conducting sphere, Radius is R, total charge is Q. The electric potential is a function of ____. The electric field is a function of ____

Suppose there are many source charges, q₁, q₂... the electric potential V at a point in space is the ____ of the _______ due to each charge. So V = _____ = _____
Define r_i  
The electric potential is a simple _____ ____ which is easier to find

Label the diagram  (4)

Vector E and V are not two distinct entities, but instead, two different perspectives or two different mathematical representations of?
Vector E at a point is _______ to the equipotential surface at that point 
Vector E points in the direction of _______ potential

Vector E is ______ to the equipotential surface everywhere. Vector E points ______ in  the direction of ______ V. The field strength is ________ ________ to the spacing d between the equipotential surfaces

A positive charge speeds up as it moves from ______ to ______ potential. The work required to move a charge, at a ______ _____, in a direction opposite the electric field is: 
W = ______ = _____ = _____
Constant speed → F_hand = ____ = ____
Thus  = ____ (explain d)

Below are the three important arrangements of charges. Both electric field lines and equipotentials are shown. Remember the electric field vector is ______ to the equipotential surface. 
In point charges and electric dipoles, field lines are everywhere _________ to equipotentials. The electric field is _______ where the equipotentials are closer together. For electric dipoles in a Parallel-plate capacitor, field lines point from ______ to ______ potential. For the capacitor, the field is ______ and so the equipotential spacing is _______

Properties of a conductor in electrostatic equilibrium: 
1. All excess charge is on the ______
2. The electric field inside is ______
3. The exterior electric field is ______ to the surface 
4. The electric field strength is largest at the ______ ______

The electrical activity of cardiac muscle cells makes the beating heart an ______ ______. A resting nerve cell is _______; the outside is ______ and the inside is ________. Initially, all muscle cells in the heart are polarized, until an electrical impulse from the heart triggers the cells to ______, moving ions through the cell wall until the outside becomes ______. This causes the muscle to contract

The depolarization of one cell triggers a wave of ________ to spread across the tissues of the heart. At any instant, a boundary divides the negative charges of _______ cells from the positive charges of cells that have not yet ________ in the heart. This separation of charges creates an electric dipole and produces a ______ ______ field and ______

The boundary between polarized and depolarized cells sweeps rapidly across the atria. At the boundary there is a charge separation. This creates an ______ ______ and an associated dipole moment 
Label the diagram

A measurement of the electric potential of the heart is an invaluable diagnostic tool. The potential difference in a patient is measured between several pairs of ________. A chart of the potential differences is the __________, also called an _____ or an _____. With each heart beat, the wave of depolarization moves across the heart muscle. The dipole moment of the heart changes _______ and _______

The records of the potential difference between the two electrodes is the ________. 
The potential differences at a, b, and c correspond to those measured in the three stages shown to below