21.2 Applications of Electric Field If you do work to lift a ball against gravity the PE of the ball will increase. The same works with charges. How do you get unlike charges apart? The farther apart the charges are moved the more work that is done and more energy is gained. Electric Potential Difference,  V, is defined as the work done in moving a positive test charge between two points in the electric field.

The difference in electrical potential is the ratio of the work needed to move a charge to the strength of that charge. Units of volt (J/C = V)

Equipotential positions Equipotential lines are similar to altitude lines on a map

The Electric Potential in a Uniform Field Use 2 plates, one charged positive and one negative The electric field is constant between the plates and the direction is from positive to negative Place a positive test charge, q’ in the field and move it a distance d towards the positive plate

W on q’ = Fd W on q’ =  Vq’ So,  V=Fd/q’=(F/q’)d  V=Ed E=  V/d So the units for E can be either N/C or V/m The electric potential increases in the direction opposite of the electric field direction The electric potential is higher near the positively charged plate

By dimensional analysis the product of the units of E and d is (N/C)(m) N. m is a J (Joule) So 1 V = 1J/C

Millikan’s Oil-Drop Experiment Used to find the charge on an electron A fine mist was sprayed into and Electric Field Gravity causes the drops to fall Field increased until drops rise Field adjusted until drops are suspended Downward force of gravity equals upward electric force

Magnitude of E determined form the electric potential difference Weight of electron had to be determined Drop was suspended and then the electric field was turned off so the drop could fall Because friction of tiny drop so large terminal velocity was reached quickly Using a complex equation the mass was found Then using mg the weight was calculated.

Sharing of Charge All systems come to equilibrium to make the energy of the system at minimum. Ball on a hill will end up resting in a valley If one object is charge and comes in contact with an uncharged object the charges with spread out evenly across both objects. If objects are not of same size then the charges equal out until voltage is the same Charges are closer together at sharper points

Storing Charges: The Capacitor Lift a book to a shelf and you increase GPE. In a sense you are storing GPE A device that stores electric potential energy is called a capacitor. As a charge is added to an object the electric potential difference between that object and the Earth increases. For a given situation the ratio of the charge stored to the electric potential difference is a constant

That ratio is called the capacitance, C The unit of capacitance is a farad, F

Farad Farad, F, named after Michael Faraday One Coulomb/volt 1 C is a very large charge so 1 F is also very large Often  F or pF

Uses Storage of charge Memory capacitors to prevent losses of memory in computers Televisions have very large capacitors Power giant lasers Small ones power a flash of a camera