68. Two point charges Figure P19.67 qA= -12.0 Mu C, and qB = 45.0 MuC and a thir

Question

68. Two point charges Figure P19.67 qA= -12.0 Mu C, and qB = 45.0 MuC and a third particle with unknown charge qc are located on the x axis. The particle qA is at the origin, and qB, is at x = 15.0 cm. The third particle is to be placed so that each particle is in equilibrium under die action of the electric forces exerted by the other two particles. (a) Is this situation possible? If so, is it possible in more than one way? Explain. Find (b) the required location and (c) the magnitude and the sign of the charge of the third particle.

Explanation / Answer

Charges q = -12 x 10 -6 C

             q ' = 45 x 10 -6 C

            q " = ?

(a). The situation is possible

(b).Let the required location is at a distance x from the charge q on negative x axis.

Force on q " due to q is equal and opposite to the force on q " due to q ' then the they are in equilibrium.

Force on q " due to q = Force on q " due to q '

Kq q " / x 2 = K q ' q " / ( r + x ) 2

Where r = 15 cm = 0.15 m

q / x 2 = q ' / ( r + x ) 2

q / q ' = x 2 / ( r + x ) 2

0.26666 = x 2 / ( 0.15 + x ) 2

x 2 = 0.2666 ( 0.15 + x ) 2

x = 0.5163 (0.15 + x)

= 0.07745 + 0.5163 x

x = 0.1601 m

   = 16.01 cm

~ 16 cm

Third partile charge is positive

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