Write the following using symbols. Be precise!
b) The magnitude of the sum of two vectors v1 and v2
A point charge Q produces an electric field E1 at
point P of magnitude 5.0 N/C and direction 45? to the x-axis,
as shown in the diagram. A second charge q produces an electric field E2
P of magnitude 8.0 N/C at 60? to the negative
What is the total electric field at point P?
The components of E1 are:
x-component: E1x = (5 N/C)cos45 = (5 N/C)/sqrt(2) = 3.54 N/C
y-component: E1y = (5 N/C)sin45 = (5 N/C)/sqrt(2)
= 3.54 N/C
The components of E2 are:
x-component: E2x = - (8 N/C)cos60 = - (8 N/C)/2 = -4.0 N/C
y-component: E2y = (8 N/C)sin60 = (8 N/C)/?3/2 = 6.93 N/C
Adding then, we get
Ex = (3.54- 4) N/C = - 0.46 N/C rounds to - 0.5 N/C
Ey = (3.54 + 6.93) N/C = 10.46 N/C rounds to 10.5 N/C
We may also give the answer as E = sqrt(0.52 + 10.52
) N/C at tan-1(10.5/.5) to the negative x-axis = 10.5
N/C at 87 degrees to the negative x-axis.