Electrical Energy and Current Electric Potential

Electrical Energy and Electric Force Work is done on a charge q as it is moved from a position A to position B when the charge is in an electric field E. This gives the charge electrical potential energy. When the charge is released from position B, the electrical force, qE, accelerates the charge through the distance d. The potential energy the charge possesses is then changed into kinetic energy.

Electrical Energy and Electric Force Electrical potential energy – potential energy associated with an object due to its position relative to a source of electric force Measured in joules (J) just like any other form of energy In atomic and nuclear physics – measured in electron volts (eV) 1eV = 1.60*10-19J Results from interaction of two objects’ charges Is a form of mechanical energy ME = KEtrans + KErot + PEg + PEelastic + PEelectric

Electrical Energy and Electric Force Electrical potential energy can be associated with a charge in a uniform field Uniform field – a field that has the same value and direction at all points Electrical potential energy for a charge in a uniform electric field Electrical potential energy = - (charge * electric field strength * displacement from the reference point in the direction of the field) PEelectric = -qEd d is only relevant when it is parallel to the electric field May have to use right triangle functions to get the parallel component of motion

Electrical Energy and Electric Force + charge charge In same direction of electric field Loses PEelectric Gains PEelectric In opposite direction of electric field

Electrical Energy and Electric Force Electrical potential energy for a pair of charges Electrical potential energy = Coulomb constant * charge 1 * charge 2 / distance PEelectric = kCq1q2/r kC = 8.99*109 N*m2/C2 When the charges have the same sign, their potential energy is positive, which corresponds to a repulsive force. When the charges have unlike sign, their potential energy is negative, which corresponds to an attractive force. As like charges are separated, the potential energy of the system decreases.

Changing Electrical Potential Electric potential – the electric potential energy associated with a charged particle divided by the charge of the particle Symbolized by V and measured in volts (V) Since larger charges have greater electric potential energies than smaller ones, the ratio of electric potential energy to charge remains the same for all charges at a point Electric potential is independent of charge Electric potential = (Electrical potential energy) / charge V = PEelectric / q

Changing Electrical Potential Potential difference – the change in electrical potential energy associated with that charge divided by the charge of the particle Ratio of change in electrical potential energy to charge Symbolized by ΔV and measured in volts (V) 1V = 1J/C Named in honor of Alessandro Volta who developed the first practical battery Often called voltage Small batteries typically have a potential difference of 1.5V, car batteries 12V, electrical outlets 120V

Changing Electrical Potential Potential difference = -(magnitude of the electric field * displacement) ΔV=-EΔd Remember, we only care about displacement parallel to the direction of the electric field

Changing Electrical Potential Potential difference between a point at infinity and a point near a point charge Potential difference = Coulomb constant * (value of the point charge) / (distance to the point charge) ΔV = kCq/r Must have a reference point for determining electric potential Typically assume Earth has a zero value for electric potential Grounding – connecting an electrical device to Earth creates such a reference point

Changing Electrical Potential To get the resultant potential difference for a group of charges, just add them up, keeping track of the signs Called the superposition principle Positive charges have positive electric potentials Negative charges have negative electric potentials Electric potential is a scalar so don’t have to worry about x and y components

Changing Electrical Potential Batteries must do work to move charges across a potential difference Batteries have two terminals One positive and one negative One positive and one grounded Charges naturally move from positive to negative terminal in a circuit Work must be done on the charges to move back to positive terminal Batteries give the charge energy to move back across the potential difference