   Chapter 15, Problem 24P

Chapter
Section
Textbook Problem

(a) Find the magnitude and direction of the electric field at the position of the 2.00 μC charge in Figure P13.13. (b) How would the electric field at that point be affected if the charge there were doubled? Would the magnitude of the electric force be affected?

(a)

To determine
The magnitude and direction of net electric field on 2μC .

Explanation

The force diagram is given by,

In the above diagram,

• F1 is the force due to q1 on q2 .
• F3 is the force due to q3 on q2 .

Formula to calculate the force due to q1 on q2 is,

F1=keq1q2a2      (I)

• ke is the Coulomb constant.
• a is the side of the triangle

Formula to calculate the force due to q3 on q2 is,

F3=keq3q2a2       (II)

Net force along the x direction is,

Fx=F3F1cos60ο       (III)

Net force along the y direction is,

Fy=F1sin60ο       (IV)

Formula to calculate the magnitude of net electric force is,

FR=Fx2+Fy2       (V)

Substitute Equations (III) and (IV) in (V).

FR=(keq3q2a2(keq1q2a2)cos60ο)2+(keq1q2a2sin60ο)2=(keq2a2)(q3q1cos60ο)2+(q1sin60ο)2

Formula to calculate the resultant electric field is,

ER=FRq2

Therefore,

E=(q2a2)(q3q1cos60ο)2+(q1sin60ο)2

Substitute 8.99×109N.m2/C2 for ke , 7.00μC for q1 , 2.00μC for q2 , 4.00μC for q3 and 0

(b)

To determine
The electric field if the charge is doubled.

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