Question

Three identical metal spheres are hung from a ceiling on rigid non-conducting rods. Sphere 1, sphere 2, and sphere 3 have charges 71 µC, −52 µC, and 46 µC, respectively. Each sphere is separated by 17 cm.
(a) What is the net electric force on the middle sphere due to spheres 1 and 3? (Enter the magnitude only.)(b) What is the direction of the net electric force?
a. up
b. down
c. left
d. right
e. no direction (zero magnitude)

Answer 1

Answer:

a) The net electric force on the middle sphere due to spheres 1 and 3 is 404N. b) The direction of the net electric force is to the left.

Explanation:

In order to solve this problem, we must first draw our free body diagram (See attached picture).

By definition, two opposite charges attract each other, so the force due to sphere 1 will go to the left (being the left direction negative) and the force due to sphere 3 will go to the right (being the right direction positive).

Knowing this we can use the electric force formula to calculate each of the forces:

$F_{e}=k_{e}\frac{q_{1}q_{2} }{r^{2} }$

where $k_{e}$=$8.99x10^{9}N\frac{m^{2} }{C^{2} }$

So knowing this, we can now calculate each force. Let's start with the force exerted by sphere 1 over sphere 2:

$F_{12}=8.99x10^{9}N\frac{m^{2} }{C^{2} }\frac{(71x10^{-6}C)(52x10^{-6}C) }{(0.17m)^{2} }$

Which gives me a force of:

$F_{12}=-1148.48N$

In this case the force will be negative because it's directed towards sphere 1, this is to the left.

We can do the same with the force due to sphere 3:

$F_{23}=8.99x10^{9}N\frac{m^{2} }{C^{2} }\frac{(46x10^{-6}C)(52x10^{-6}C) }{(0.17m)^{2} }$

Which gives me a force of:

$F_{23}=744.09N$

In this case the force is positive because it's directed towards sphere 3, this is it goes to the right.

With these two values I can now find the net force electric force on the middle sphere due to spheres 1 and 3.

$F_{net}=$∑F

$F_{net}=F_{12}+F_{23}$

$F_{net}=-1148.48N+744.09N$

$F_{net}=-404.39N$

a) Since part a of the problem only asks us for the magnitude, then the net electric force on the middle sphere due to spheres 1 and 3 is 404.39N

b) since the answer when solving this problem was negative, this means that the force will be directed towards sphere 1, this is to the left.