   Chapter 15, Problem 30P

Chapter
Section
Textbook Problem

Three point charges are located on a circular are as shown in Figure P15.30. (a) What is the total electric field at P, the center of the are? (b) Find the electric force that would be exerted on a −5.00-nC charge placed at P. Figure P15.30

(a)

To determine

To determine: The total electric field at P.

Explanation

Explanation:

At the point P, the directions of electric fields are-

• E+ is the electric field due to 3.00 nC charge.
• E is the electric field due to -2.00 nC charge.

The vertical sine components of 3.00 nC charge get cancelled. The horizontal components of 3.00 nC get added. The electric field due to -2.00 nC is towards the left. Therefore, the net electric field is,

Enet=2E+cos30οE       (I)

Formula to calculate the electric field due to 3.00 nC is,

E+=keQr12       (II)

• ke is the Coulomb constant.
• Q is the charge.
• r1 is the distance between the positive charge and the point P.

Formula to calculate the electric field due to -2.00 nC is,

E=keqr22       (III)

• ke is the Coulomb constant.
• q is the charge.
• r2 is the distance between the negative charge and the point P.

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

Enet=2(keQr12)cos30ο(keqr22)

Substitute 8.99×109N.m2/C2 for ke , 3.00 nC for Q, -2.00 nC for q, 4.00 cm for r1 and 4.00 cm for r2 .

Enet=2[(8

(b)

To determine
The electric force on -5.00 nC at P.

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