1. Electric Field PH 203 Professor Lee Carkner Lecture 2

2. Force on Charges  F y = 8.99X10 9 (4)(2)/(2 2 ) = 1.8X10 10 N  F x = 8.99X10 9 (2)(5)/(3 2 ) = 1X10 10 N  F 2 = F x 2 + F y 2  F = 2.1X10 10 N  tan  = (F y /F x )   = arctan (F y /F x )   = 61 degrees 3 m 2 m q 2 = 5 C q 3 = 4 C q 1 =-2 C 

3. The Electric Field  The electrical force acts at a distance   The area where a force may exist is said to be occupied by an electric field   We imagine a small test charge (q 0 ) at various locations around the main charge (q)  The test charge is small enough so that its field does not affect the main one

4. Defining the Electric Field  The electric field is defined as the force on the test charge per unit charge or: E = F/q 0   We can then write the force on the object with Coulomb’s law and so we get: E = k q/r 2   This equation is only true for point charges

5. Electric Field Direction  We can also write k as 1/(4  0 )  Where  0 is the permittivity of free space = 8.85 X 10 -12 C 2 /Nm 2   E also has a direction   Note that free charges are often negative and so move in the opposite direction as the field

6. Calculating the Electric Field   Need to find the magnitude and direction of the field from each charge and add vectorially   Note that once you find the value of the electric field, the force on a charge q 0 at that point is just F=Eq 0

7. Field Lines   The field lines are a “map” of how the charge will effect other charges   Field lines indicate how a charge will move

8. Field Lines and the Field  What is the force on a charge in a field  Direction:   At any point the F vector is tangential to the field lines  Strength:   Density of lines proportional to field strength

9. Example of Fields

10. Dipole   Called a dipole   Occurs naturally in molecules or when charges are pulled apart but can’t physically separate  Magnetic fields are always dipolar

11. How to Draw Field Lines  Lines determine the force experienced by a positive charge   Number of lines touching a charge proportional to the magnitude of the charge  More charge, more lines 

12. Next Time  Read 22.5-22.9  Problems: Ch 22, P: 9, 12, 13, 30, 50

13. Consider two charges a certain distance apart. If the distance is doubled and one of the charges has its magnitude doubled, the new force compared to the old force is, A)¼ B)½ C)1 (force is unchanged) D)2 E)4

14. A free charge +Q is placed exactly midway between a fixed charge –Q to its left and a fixed charge +Q to the right. Which direction will the free charge move in (all Q’s have the same magnitude)? A)Left B)Right C)It will not move D)It depends on the specific value of Q E)You can’t tell from the information given