Question

 

The following charges exist (given coordinates are (x, y) coordinates in the plane of the page):

• a −3.0 µC point charge located at (0, 0)

• a −2.0 µC uniform spherical shell of charge of radius 3.0 cm centered at (+4.0 cm, 0)

• a +2.0 µC uniform spherical shell of charge of radius 2.0 cm centered at (0, −4.0 cm)

• a +4.0 µC uniform spherical shell of charge of radius 4.0 cm centered at (−1.0 cm, +1.0 cm)

(a). Calculate the net electric force (magnitude and direction) acting on the −3.0 µC point charge.

(b). Suppose you were given a +1.0 µC charge to add to the arrangement of charges above. Your goal is to place the charge so that the net force on the −3.0 µC charge is zero. Where would you put the +1.0 µC charge? Be specific.

(c). The −3.0 µC point charge was created by either adding or removing electrons from a neutral object. Were electrons added or removed? How many electrons were added or removed?

Answer 1

Electric field inside the Shell is given by,

Electric field outside the shell is given by,

According to the charge distribution given in question, you can see in the figure that,

point (0,0) is inside the shell (3) while outside of the shell (1) and (2),

So that, Electric field at the origin is given by,

Here, E3 = 0

Here,

So that,

Here, Charge on origin is -3 micro coulomb. So that,

PART - B

Here, we want to add +1 micro coulomb charge such that the force on the charge -3 micro coulomb becomes zero, So that,

the force acts due to +1 micro coulomb charge on the charge -3 micro coulomb must be,

......(1)

Suppose, the charge +1 micro coulomb placed at position (x,y) then, force due to charge +1 micro coulomb on the origin is given by,

......(2)

By comparing x-component and y-component of equation (1) and equation (2) ,

From above expression we can see that,

So that, by putting x = y in above expression,

here, x = y so that,

PART - C :

charge can be obtained by adding the electrons to the object.