14. +-11 points OSUniPhys1 22.3.WA.025. My Notes + Ask Your Tea Two small copper

Question

14. +-11 points OSUniPhys1 22.3.WA.025. My Notes + Ask Your Tea Two small copper spheres, identical in size, have charges q-16.0 HC and q2+51.0 uC, and are located in the x-y plane at (0, 4.40) cm and (2.60, 0) cm respectively. (Express your answer in vector form. Do not enter units in your expression. Assume the spheres may be approximated as point charges.) (a) Find the force qi exerts on qz (b) The two copper spheres are briefly brought into contact and then moved back to their original locations. Now what force does q1 exert on q2? Additional Materials

Explanation / Answer

A)

Force on q2 due to q1:

F21 = k*q1*q2/(r)

= 9*10^9*16*10^-6*(51*10^-6)/sqrt(.044^2+.026^2)

= 143.7 N

Direction = 180 - atan(4.4/2.6)

= 120.6 deg

So, in vector form,  

F21 = 143.7(cos(120.6 deg) i + sin(120.6 deg) j)

= (- 73.1 i + 123.7 j) N

B)

Now, the charges on both will be same.

Charge on each = (51-16)/2 =17.5 uC

So, force on q2 due to q1:

F21 = 9*10^9*(17.5*10^-6)^2/(. 044^2+.026^2)

= 53.9 N

Direction = - 59.4 deg

So, in vector notation,  

F21 = 53.9*cos(-59.4deg) i + 53.9*sin(-59.4deg) j

= (27.4 i - 46.4 j) N

B)

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