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ELECTRIC FIELD (Section 19.5) Electric fields due to point charges for now (will do more later) Imagine an arrangement of point charges in space Force on a small positive charge q3 at P Force on a small negative charge q4 at P Don’t need a different vector sum for each different charge at P! Force on a small positive charge q3 at P Force on a small negative charge q4 at P Define ELECTRIC FIELD at P: F3 F4 Eat P q3 q 4 Charges q1 and q2 cause an electric field at P The electric field at P is independent of charge at P ELECTRIC FIELDS: IMPORTANT CONCEPTS Any point charge q creates an electric field at all surrounding points in space If the electric field at a point in space is E , then the force on a charge q0 at that point is F q0 E o F is in the same direction as E for positive q0 o F is in the opposite direction from E for negative q0 q If the electric force on a charge 0 at a point in space is known to be F F o then the electric field at that point must be E q 0 o The units of electric field are N/C Force and Electric Field are both VECTORS Direction for Force and Electric Field: another special unit vector r̂ For the ELECTRIC FORCE on a charge at P due to a charge q: Unit vector r̂ points from q → P qq0 F k rˆ e 2 Force is qq0 r o Points in same direction as r̂ if q and q0 have the same sign o Points in opposite direction to r̂ if q and q0 have opposite signs For the ELECTRIC FIELD at P due to a charge q: Fqq0 q ˆ E k e 2 r Electric field at P is P q0 r o Points in same direction as r̂ if q is positive ( E points away from +) q r̂ o Points in opposite direction to if is negative ( E points toward -) Superposition: Because Electric Field is a vector: The total E at any point P due to a particular arrangement of point charges is the VECTOR SUM of the electric field vectors due to all charges around P Total electric field at P is: q rˆ ET k e i 2 i E1 E2 E3 E4 ri i o q i is the charge at i o ri is the distance from q i → P o r̂i is the unit vector from q i → P o the sum is a VECTOR SUM The Electric Dipole is an important arrangement of charges charges q and q separated by distance 2a o Charges in some molecules (polarizable) separate in an electric field Result is an induced electric dipole responsible for van der Waal’s interaction o Many molecules have permanent electric dipoles (i.e. water) o Insulators in which dipoles can be induced are used in capacitors dielectrics Example: (a) Show that the electric field at point P a distance y above the midpoint of an electric dipole aligned along the x-axis is: 2k e q a ˆ EP i 2 2 3/ 2 a y (b) Show that the electric field at point P a distance x along the x-axis from the midpoint of an electric dipole aligned along the x-axis is: 1 1 ˆ EP ke q i 2 2 x a x a (c) Using 1 x n 1 nx nn 1 x 2 , show that for part (b) becomes 2 4k q a E P e3 iˆ x x>>a the answer in For point charges: calculate contributions to total electric field at a point in space from each point charge separately o then find total electric field by doing a vector sum. For a continuous charge distribution (i.e. a line of charge, a charged surface, or a charged volume) Break charge distribution into small elements o treat each element as a point charge. Write a vector sum of contributions from all elements Take limit as elements become infinitesimally small o Sum becomes an INTEGRAL! (but don’t panic. You will be shown how to evaluate) We will come back to do electric fields due to continuous charge distributions later!