physics chapter 22.5-22.6 point charges + electric vs gravitational fields

a point charge

a convenient expression for a charged object in a situation where distances under consideration are much greater than the size of the object

a test charge in an electric fields

a point charge that doesn't alter the electric field in which it is places

when would an electric field be altered due to an object being placed in the field

if an object had sufficiently large charge that it causes a change in the distribution of charge that creates the field

equation for the electric field strength at distance r from a point charge +Q

E = Q/4𝛑ε0r^2 --> if Q is negative, the equation gives a negative value of E = corresponds to the field lines pointing inwards towards Q

the resultant electric field strength due to forces in the same direction

E = F/Q = (QE1 + QE2)/Q = E1 + E2

the resultant electric field strength due to force in opposite directions

E = F/Q = (QE1 - QE2)/Q = E1 - E2

the resultant electric field strength due to forces at right angles to each other

E = F/Q --> E^2 = (F1^2 + F2^2)/Q --> E^2 = E1^2 + E2^2

how to calculate resultant electric field strength in general

the vector sum of the individual electric field strengths

the electric field lines of force surrounding a point charge Q, + so the equipotentials around Q

radial electric field lines, + so the equipotentials are concentric circles centred on Q

relationship between electric field strength and distance from a charge Q, + so what the curve of the graph of distance against electric field strength is

the electric field strength is inversely proportional to the square of the distance r --> curve = an inverse square law curve

equation for the electric potential V at distance r from Q

V = Q/4𝛑ε0r

relationship between electric potential V and distance r

V is inversely proportional to r

why is the gravitational potential in a gravitational field always negative

because the force is always attractive

why can the electric potential in an electric field near a point charge Q be positive or negative

because it depends on whether Q is a positive or a negative charge

what does the gradient of an electric potential against distance graph show

the negative of the electric field strength

what does the area under an electric field strength against distance graph show

the change of potential

what does a graph of electric field strength against distance show, + why

shows how the force per unit charge on a positive test charge varies with distance, because electric field strength is the force per unit charge on a small positive test charge

line of force/field line for a gravitational field and for an electric field

g = path of a free test mass in the field; E = path of a free positive test charge in the field --> similar

inverse square law of force equation for a gravitational field and for an electric field

g: F = Gm1m2/r^2; E: F = Q1Q2/4𝛑εor^2 --> similar

field strength equation for a gravitational field and for an electric field

g = force per unit mass = F/m; E = force per unit +charge = F/Q --> similar

unit of field strength for a gravitational field and for an electric field

g = N/kg = m/s^2; E = N/C = V/m --> similar

uniform fields for a gravitational field and for an electric field

g = the same everywhere, with field lines being parallel and equally spaced; E = the same everywhere, with field lines being parallel and equally spaced --> similar

potential for a gravitational field and for an electric field

g: potential = gravitational potential energy per unit mass; E: potential = electric potential energy per unit +charge --> similar

unit of potential for a gravitational field and for an electric field

g: potential = J/kg; E: potential = V = J/C --> similar

equation for potential energy of 2 point masses or charge for a gravitational field and for an electric field

g: Ep = -Gm1m2/r; E: Ep = Q1Q2/4𝛑εor --> similar

radial fields for a gravitational field and for an electric field

g: due to a point mass or a uniform spherical mass M, g = GM/r^2 and V = -GM/r; E: due to a point charge Q, E = Q/4𝛑ε0r^2 and V = Q/4𝛑ε0r --> similar

action at distance r for a gravitational field and for an electric field

g = action is between any 2 masses; E = action is between any 2 charged objects --> different

force (attractive or repulsive) for a gravitational field and for an electric field

g = attractive only; E = unlike charges attract and like charges repel --> different

constant of proportionality in force law for a gravitational field and for an electric field

g = G; E = 1/4𝛑ε0 --> different