# resolução

(Parte 4 de 11)

Express the force that q1 exerts on

Express the force that q2 exerts on q4:

qkq=r , whereis a unit vector

Chapter 21 14

jir r r

jiF

Substitute and simplify to find 4Fr :

31 ••

Picture the Problem The configuration of the charges and the forces on q3 are shown in the figure … as is a coordinate system. From the geometry of the charge distribution it is evident that the net force on the 2 µC charge is in the negative y direction. We can apply

and then add them to find the net force on q3.

The Electric Field 1: Discrete Charge Distributions 15

Express the force that q1 exerts on

where r qkqF

and

Express the force that q2 exerts on

and

simplify to obtain: j j ijiF

Substitute numerical values and

evaluate 3Fr :

() j jF

 for its distance from the origin

*32 •• Picture the Problem The positions of the charges are shown in the diagram. It is apparent that the electron must be located along the line joining the two charges. Moreover, because it is negatively charged, it must be closer to the −2.5 µC than to the 6.0 µC charge, as is indicated in the figure. We can find the x and y coordinates of the electron’s position by equating the two electrostatic forces acting on it and solving

We can use similar triangles to express this radial distance in terms of the x and y coordinates of the electron.

Chapter 21 16 satisfied if the electron is to be in equilibrium:

Express the magnitude of the force

that q1 exerts on the electron:

Express the magnitude of the force

that q2 exerts on the electron:

eqk Fe=

Substitute for q1 and q2 and simplify:

Solve for r to obtain:

Because r < 0 is unphysical, we’l consider only the positive root.

Use the similar triangles in the diagram to establish the proportion involving the y coordinate of the electron:

Use the similar triangles in the diagram to establish the proportion involving the x coordinate of the electron:

The Electric Field 1: Discrete Charge Distributions 17

Picture the Problem Let q1 represent the charge at the origin, q2 the charge at (0, 0.1 m), and q3 the charge at (0.2 m, 0). The diagram shows the forces

acting on each of the charges. Note the action-and-reaction pairs. We can apply Coulomb’s law and the principle of superposition of forces to find the net force acting on each of the charges.

Express the force that q2 exerts on q1:

qkq

r qkqr

r r are action-and-reaction forces.

Chapter 21 18

Express the force that q3 exerts on q2:

r qkq qkq r ) jiF

Find the net force acting on q2:

express the net force acting on q3:

Picture the Problem Let q1 represent the charge at the origin and q3 the charge initially at (8 cm, 0) and later at (17.75 cm, 0). The diagram shows the forces

acting on q3 at (8 cm, 0). We can apply Coulomb’s law and the principle of superposition of forces to find the net force acting on each of the charges.

Express the net force on q2 when it is at (8 cm, 0):

r F r r

rQr qkq r qkQr qkq

(Parte 4 de 11)