Electricity Tip Sheet

Electricity Tip Sheet There are several terms in the electricity chapters that look very similar but are not the same thing. Be sure to distinguish among them. A common method to get no credit on a question is to solve for the wrong thing. There are four basic quantities that can be calculated for electricity:

Property of Space Interaction

Vector Electric Field (E) in newtons/coulomb (N/C) Electric Force (Fe) in newtons (N) Scalar Electric Potential (V) in volts (V) Electric Potential Energy (U) in joules (J)

Vector Approach

Electric Field

Charged objects create an electric field, E, everywhere in space. It points away from positive charges and towards negative charges, by convention (you may need to use trigonometry to obtain a specific direction). Its magnitude varies depending on its configuration. Here are some common configurations:

Configuration Formulas Point charge (also outside a spherically E = k|q|/r2 symmetric charge distribution or any net k = 8.99E9 Nm2/C2 charge where r >> size of object) q = net charge r = distance between charge and point in space Dipole (when r >> size of dipole) E = 2kp/r3 (on dipole axis) E = kp/r3 (perpendicular to dipole axis) p = electric dipole moment = q*d (or empirical value) q = magnitude of charge at one end of dipole d = distance between + and - charges Long line (r << L) E = 2kλ/r λ = q/L L = length of line

Large sheet (r << dimensions of sheet) E = σ/(2ε0) σ = q/area (also denoted η) 2 2 ε0 = 8.854E-12 C /(Nm )

If there is more than one charged object, then use vector sums to calculate the net electric field. It cannot be emphasized enough that you must use vector sums.

Electric Field Lines

Electric field lines are used to create pictures approximating the magnitude and direction of the electric field at a variety of locations. The rules for creating such a picture are as follows:

 Field lines radiate outwards from positive charge and terminate at negative charge  The number of field lines originating or terminating is proportional to the charge

 Field lines do not cross

 Field lines are perpendicular to equipotential surfaces

Once you have field lines, you can estimate the magnitude of the field by the density of the lines and the direction of the field by the direction of the lines.

Electric Force

The electric field at a given location can be used to calculate the electric force, Fe, on a point charge at that location.

Fe = qE

The formulas for point charges can be combined into Coulomb’s law (which is a special case for point charges):

2 Fe = k|q1q2|/r

The direction is away for like charges and towards for opposite charges (you may need to use trigonometry to obtain a specific direction).

If there is more than one force, then use vector sums to calculate the net force. It cannot be emphasized enough that you must use vector sums.

Electric forces can sometime be used to solve problems with Newton’s laws. But it is not usually possible to use constant acceleration kinematics as the field and force usually vary with distance. One exception is with charged plates which create constant fields and constant forces over reasonable distances.

Scalar Approach

Charged objects create an electric potential, V, everywhere in space. The sign of the electric potential will be determined by the sign of the charge, so be sure to include signs when using these formulas. Electric potential due to a point charge can be calculated as follows:

V = kq/r

If there is more than one point charge, then add the potentials.

The electric potential energy, U, due to the interaction of a point charge, q, with other charged objects creating an electric potential, V, at its location can be calculated as follows:

U = qV

This can be combined with the formula for electric potential to obtain a formula for the energy due to the interaction of two point charges (a special case): U = kq1q2/r

Electric potential energy can be used to solve problems with the law of conservation of energy (see the general tip sheet).

Relationships between Scalar and Vector Quantities

Es = -∂V/∂s ≈ -ΔV/Δs (Es = “s” component of electric field)

ΔV = -∫Esds

Fs = -∂U/∂s ≈ -ΔU/Δs (Fs = “s” component of electric force)

ΔU = -∫Fsds

These are formulas that are not often used on homework or exams, though they are used to derive other useful formulas. For example, the magnitude of the potential difference between two charged sheets separated by a distance d is derived from the formula for the electric field of a sheet:

ΔV = σd/ε0