   Chapter 15, Problem 11P

Chapter
Section
Textbook Problem

Three charges are arranged as shown in Figure P15.11. Find the magnitude and direction of the electrostatic force on the charge at the origin. To determine
The magnitude and direction of electrostatic force at the origin.

Explanation

The force diagram is given by,

In the above diagram,

• F3 is the force due to -3 nC charge on the 5 nC charge.
• F6 is the force due to 6 nC charge on 5 nC charge.

Formula to calculate the force due to -3 nC charge on the 5 nC charge is,

F3=keq0q2r022      (I)

• ke is the Coulomb constant.
• r02 is the distance between origin and -3 nC charge.

Formula to calculate the force due to 6 nC charge on the 5 nC charge is,

F6=keq0q1r012       (I)

• ke is the Coulomb constant.
• r01 is the distance between origin and 6 nC charge.

Formula to calculate the magnitude of electrostatic force at the origin is,

FR=F32+F62       (III)

Substitute Equations (I) and (II) in (III).

FR=(keq0q2r022)2+(keq0q1r012)2=keq0(q2r022)2+(q1r012)2      (VI)

Substitute 8.99×109N.m2/C2 for ke , 6nC for q1 , 3nC for q2 , 5 nC for q0 , 0.100 m for r02 and 0.300 m for r01 .

FR=(keq0q2r022)2+(keq0q1r012)2=(8.99×109N.m2/C2)(5nC)(3nC(0

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