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[Grade 12] electric forces?
"Four charged spheres, with equal charges of 2.20 Cb are situated at the four corners of a rectangle with a length of 0.4 meters and a width of 0.3 meters. what is the net electrostatic force on the charge in the top right corner?"
According to the book, the answer is '7.17*10^11 Newtons 55.0 degrees' I don't know how to add the vectors properly to get that. I can get the effect from the charge below and to the left, but I don't know how to do the charge diagonally down and how to add it. any help would be greatly appreciated.
1 Answer
- Steve4PhysicsLv 74 years ago
The symbol for a coulomb is 'C', not 'Cb'.
Suppose the rectangle is:
A. . B
C. . D
with AB = CD = 0.4m and AC = BD = 0.3m.
The diagonal is BC = AD = 0.5m (3-4-5 triangle)
Or do it the long way using Pythagoras:
BC² = 0.4² + 0.3² = 0.25
BC = 0.5m
Note that if we call angle ABC, ‘θ’ then
sinθ = AC/CB = 0.3/0.5 = 0.6
cosθ = AB/CB = 0.4/0.5 = 0.8
____________________
I’ll use exponential notation so, for example, 3x10⁸ is written as 3e8.
Force on qB from qA is k.qA.qB/r² = 8.99e9 * 2.20 * 2.20 /0.4² = 2.719e11 N
This repulsive force on qB acts from A to B, in the +x direction so has:
x component = 2.719e11 N
y component = 0
Force on qB from qD is k.qD.qB/r² = 8.99e9 * 2.20 * 2.20 /0.3² = 4.835e11 N
This repulsive force on qB acts from D to B, in the +y direction so has:
x component = 0
y component = 4.835e11 N
Force on qB from qC is k.qC.qB/r² = 8.99e9 * 2.20 * 2.20 /0.5² = 1.74e11 N
This repulsive force on qB acts from C to B so has:
x component = 1.74e11cosθ = 1.392e11 N
y component = 1.74e11sinθ = 1.044e11 N
Total of x components: X = 2.719e11 + 0 + 1.392e11 = 4.111e11 N
Total of y components: Y = 0 + 4.835e11 + 1.044e11 = 5.879e11 N
Resultant force F = √(X² + Y²)
= √(4.111e11² + 5.879e11²) = 7.17e11 N
The angle α of F (anticlockwise from the x axis) is given by:
tan(α) = Y/X = 5.879e11/4.111e11 = 1.43
α = tan⁻¹(1.43) = 55.0°
Adding vectors using components as above is a basic skill need for many problems. If you are unsure about adding vectors this way, try the video in the link.
Source(s): https://www.youtube.com/watch?v=eIYJSHlH4TE


