Physics 230 Spring 2001

Class Exercise Feb 2

Question: A charge q1 = 1m C is at the origin.  A second charge q2 is at x = 3 m on the x-axis. Find the electric field at point P with coordinates x = 0 , y = 1 m.

Solution

We need to find the electric field produced by each charge and add them.

The field E1 is the easier to find, since it points along the y-axis:
E1= k(1 microC)/(1 m2)j
where the j should have a hat on it because it is a unit vector.

The distance r2 from the 4 microC charge to P is sqrt(10) m (10 =12 + 3by Pythagoras' theorem) and the the second electric field contribution is:

E2= k(4 microC)/(10 m2)r
where r hat is the unit vector along the line from the charge to P.  To add the vectors, I'll do it one component at a time. Then:

Ex = -E2 cos (angle between E vector and x-axis)
= - k(4 microC)/(10 m2)(3/sqrt(10))
= - (9x109   N.m2/C2)(4 microC)(3)/(10sqrt(10) m2)
= - 3.4x103 N/C

The y component is:
Ey = E1 + E2 sin (angle between E vector and x-axis)
= k(1 microC)/(1 m2) + k(4 microC)/(10 m2)(1/sqrt(10))
=(9x109   N.m2/C2)[1 microC/m2 + (4 microC)(1)/(10sqrt(10) m2)]
=1.0x104 N/C
Notice that the x-component is negative.