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
= 0 , y = 1 m.
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 + 32 by 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)
The y component is:
Ey = E1 + E2 sin (angle between
E vector and x-axis)
= - k(4 microC)/(10 m2)(3/sqrt(10))
= - (9x109 N.m2/C2)(4
= - 3.4x103 N/C
= k(1 microC)/(1 m2) + k(4 microC)/(10 m2)(1/sqrt(10))
microC/m2 + (4 microC)(1)/(10sqrt(10) m2)]
Notice that the x-component is negative.