   Chapter 15, Problem 68AP

Chapter
Section
Textbook Problem

Three identical point charges, each of mass m = 0.100 kg, hang from three strings, as shown in Figure P15.68. If the lengths of the left and right strings are each L = 30.0 cm and if the angle θ is 45.0°, determine the value of q. Figure P15.68

To determine

The value of q.

Explanation

Given info: The mass of the charges is 0.100 kg. The length of the string is 30.0 cm.

The free body diagram is,

• FE is the net electric force.
• T is the tension.
• m is the mass of the ball.
• g is the acceleration due to gravity.

From the diagram,

Tcos45ο=mg (1)

Tsin45ο=FE (2)

Dividing the equation (2) by equation (1),

FE=mgtan45ο

Formula to calculate the net electric force is,

FE=keq2r12+keq2r22

• ke is the Coulomb constant.
• r1 and r2 are the distances of separation.
• q is the charge.

The distances between the spheres are,

r1=Lsin45οr2=2Lsin45ο

Therefore,

5keq24L2sin245ο=mgtan10ο

On Re-arranging,

q=2Lsin45οmgtan45ο5ke

Substitute 9

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