Coulomb’s Law Like charges repel, and unlike charges attract The force is proportional to the charges It depends on distance q1 q2 Other ways of writing this formula The r-hat just tells you the direction of the force When working with components, often helps to rewrite the r-hat Sometimes this formula is written in terms of a quantity0 called the permittivity of free space
Now it’s your turn Sample Problem 3.0 mC Three charges are distributed as shown at right. Where can we place a fourth charge of magnitude 3.0 mC such that the total force on the 1.0 mC vanishes? 3.0 mC ? 1.0 mC 2.0 mC 1.0 m 1.16 m 2.0 m Now it’s your turn -4.0 mC
Forces From Continuous Charges If you have a spread out charge, it is tempting to start by calculating the total charge Generally not the way to go The charge of the line is easy to find, Q = L But the distance and direction is hard to find To deal with this problem, you have to divide it up into little segments of length dl Then calculate the charge dQ = dl for each little piece Find the separation r for each little piece Add them up – integrate For a 2D object, it becomes a double integral For a 3D object, it becomes a triple integral q r dl
The units for electric field are N/C The Electric Field Suppose we have some distribution of charges We are about to put a small charge q0 at a point r What will be the force on the charge at r? Every term in the force is proportional to q0 The answer will be proportional to q0 Call the proportionality constant E, the electric field q0 r The units for electric field are N/C It is assumed that the test charge q0 is small enough that the other charges don’t move in response The electric field E is a function of r, the position It is a vector field, it has a direction in space everywhere The electric field is assumed to exist even if there is no test charge q0 present
Electric Field From a Point Charge q q0 From a single point charge, the electric field is easy to find It points away from positive charges It points towards negative charges - +
Electric Field from Two Charges Electric field is a vector We must add the vector components of the contributions of multiple charges + + - +