http://imgur.com/a/3MrC0 The above URL takes you to an image of the diagram. Thi
ID: 1530001 • Letter: H
Question
http://imgur.com/a/3MrC0
The above URL takes you to an image of the diagram. This problem has to do with electric charges and forces.
Positive charges 4q and q are distance L apart. Let them be on the x-axis with 4q at the origin. Suppose a proton were placed on the x-axis to the right of q. Is it possible that the net electric force on the proton is zero? Explain. On the figure, draw a proton at an arbitrary point on the x-axis to the left of q, between 4q and q. Draw two force vectors and label them F^rightarrow _4q and F^rightarrow_q to show the two forces on this proton. Is it possible that, for the proper choice of r, the net electric force on the proton is zero? Explain. Write expressions for the magnitudes of forces F^rightarrow _4q and F^rightarrow _q. Your expressions should be in terms of K, q, e, L, and r. F^rightarrow _4q = ______ F^rightarrow _q = _______ Find the specific position-as a fraction of L-at which the net force is zero.Explanation / Answer
a)Yes it is possible that the net electric force on proton is zero. This may happen only if, the net force on proton due to 4q and q is zero. So the following condition should get satisfied.
F4q = Fq
b) F4q = Fq
K +e 4q/ (L - r)^2 = k +e q/ r^2
4r^2 = (L - r)^2
4 r^2 = L^2 + r^2 - 2 Lr
3 r^2 + 2 Lr - L^2 = 0
r = [ -2 L +/- sqrt (4L^2 + 4 x 3 x 2L)]/12 [using x = -b +- sqrt (b^2 - 4ac)]/2a
c)F4q = k +e 4q/(L- r)^2
Fq = k +e q/r^2
d)found in part b
r = [ -2 L +/- sqrt (4L^2 + 4 x 3 x 2L)]/12
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