
Calculating the Electric Potential
Knowing the potential energy, we can calculate the electric potential of a charge q at a point using what equation?
V = U_{e}/q

The parallelplate 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
 E = Q/ε_{0}A
 (x = 0)
 negative plate
 uphill

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)
 F_{hand} = F_{e} = qE
 W = (force)(displacement) = (F_{hand})(x) = (qE)(x)
 W = ΔK + ΔU_{e} = (qE)(x)

The electric potential of the parallelplate 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} = _______ = _____
 (U_{e} = 0, V = 0)
 V = U_{e}/q = Ex = (Q/ε_{0}A)(x)
 negative plate (x = 0)
 positive plate (x = d)
 ΔV_{c} = V_{+}  V_{} = Ed

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


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
 ΔU_{e} = W_{by the hand}
 zero
 infinitely

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'
moving charge 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 yaxis is U _{elec}
 U_{e} = (k_{e})(qq'/r)
 negative
 accelerates
 infinitely
 kinetic energy
 potential energy

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)
 potential energy
 V = U_{e}/q'

 electric potential

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

 C. assume charges are positive unless told otherwise.
 Potential at point A: V_{A} = k_{e}Q/r_{A}
 Potential at point B: V_{B} = k_{e}Q/r_{B}
 V_{B}/V_{A} = (k_{e}Q/r_{B})(r_{A}/k_{e}Q) = r_{A}/r_{B} = (1mm/3mm) = 1/3

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.
 electric potential

The potential V_{0} is the potential at the surface of the charged sphere
V_{0} = _____ = _____
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

 D. V = k_{e}Q/r = (R/r)(V_{0})
 V_{0}= [(V)(r)]/(R) = (30*15)/5 = 90V


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.
 ΔV = 0
 test particle
 equipotential surface
 Because the electric field is zero inside the conductor

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, q_{1}, q_{2}... 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
 sum of the potentials

 r_{i}: the distance from charge q_{i} to the point in space where the potential is being calculated
 scalar sum

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
 Two different perspectives or two different mathematical representations of how source charges alter the space around them
 perpendicular
 decreasing

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
 perpendicular
 downhill
 decreasing
 inversely proportional

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)
 higher to lower potential
 constant speed
 W = F_{hand} = ΔU_{e} = qΔV
 F_{hand} = F_{e} = qE
 , where d is the distance between the two equipotential surfaces

D. ΔU = eΔV = e(100V) = 100 eV

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 Parallelplate capacitor, field lines point from ______ to ______ potential. For the capacitor, the field is ______ and so the equipotential spacing is _______
 perpendicular
 perpendicular
 stronger
 higher to lower potential
 uniform
 constant

 E field always points from high to low so possibly B E C
 As the E Field goes up, the distance between the lines gets smaller and smaller so C

 A: Ans = B Distance is the shortest so E field is the strongest
 B: Ans = D
 C and D check notes

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 ______ ______
 surface
 zero
 perpendicular
 sharp corners

 Wire makes it so the potential is the same in both spheres.
 v_{1} = kQ_{1}/r_{1}
 v_{2} = kQ_{2}/r_{2}
 so:
 Q_{1}/r_{1} = Q_{2}/r_{2}
 2nC/1cm = Q_{2}/2cm
 Q_{2} = 4 nC

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
 electric dipole
 polarized
 positive
 negative
 depolarize
 negative

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 ______
 depolarization
 depolarized
 depolarized
 dipole electric field and potential

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
 electric dipole

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 _______
 electrodes
 electrocardiogram
 ECG or an EKG
 magnitude and direction

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
 electrocardiogram

