Simple Nature - Light and Matter

j / Example 3.self-check AFind an equation for the magnitude of the field of a single point chargeQ. ⊲ Answer, p. 925Superposition of electric fields example 3⊲ Charges q and −q are at a distance b from each other, asshown in the figure. What is the electric field at the point P, whichlies at a third corner of the square?⊲ The field at P is the vector sum of the fields that would havebeen created by the two charges independently. Let positive x beto the right and let positive y be up.Negative charges have fields that point at them, so the charge−q makes a field that points to the right, i.e., has a positive xcomponent. Using the answer to the self-check, we haveE −q,x = kqb 2E −q,y = 0 .Note that if we had blindly ignored the absolute value signs andplugged in −q to the equation, we would have incorrectly concludedthat the field went to the left.By the Pythagorean theorem, the positive charge is at a distance√2b from P, so the magnitude of its contribution to the field isE = kq/2b 2 . Positive charges have fields that point away fromthem, so the field vector is at an angle of 135 ◦ counterclockwisefrom the x axis.k / A dipole field. Electric fieldsdiverge from a positive chargeand converge on a negativecharge.E q,x = kq cos 135◦2b2 = − kq2 3/2 b 2E q,y = kq sin 135◦2b2 = kq2 3/2 b 2The total field isE x =E y =(1 − 2 −3/2) kqkq2 3/2 b 2b 2Dipolesl / A water molecule is a dipole.The simplest set of sources that can occur with electricity butnot with gravity is the dipole, consisting of a positive charge and a564 Chapter 10 Fields