1)What is the force on the 1.0nC charge in the figure?(Figure 1) Give the magnitude. 2)Give…

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Question “1)What is the force on the 1.0nC charge in the figure?(Figure 1) Give the magnitude. 2)Give…”

Answer

Coulomb force, vector algebra are the required concepts to solve this problem.

First, using the Coulomb force, find the net force acting on

due to the two

charges. Next, use vector algebra to determine the direction of net force on

.

The Coulomb force is the force between two charges separated at a distance. The Coulomb force is.

is the Coulomb constant.

is a first charge.

is the second charge.

is the distance between them.

A vector is a physical quantity that has both magnitude and direction. A vector can be divided into a vertical and horizontal component. If the angle of the vector is measured with the horizontal axis, then the

component is the horizontal component and the

component is the vertical component, where

is the angle made by the vector with the horizontal axis.

The force on charge

due to the charge

on the left is,

Substitute

for

,

for

,

for

and

for

.

The force on charge

due to the charge

on the right is,

Substitute

for

,

for

,

for

and

for

.

Both forces are vectors. As both the charges are positive, the force

acts along the line joining charge

and the charge

on the left away from the charge. The force

acts along the line joining charge

and the charge

on the light away from the charge.

These vectors can be broken down into components so that the horizontal components are equal or opposite and then they get cancelled. The vertical components are added.

Since

is,

Substitute

for

and

and

for

.

As both the charges are positive, the force

acts along the line joining charge

and the charge

on the left away from the charge. The force

acts along the line joining charge

and the charge

on the light away from the charge.

By splitting the vectors into components, the

component of

will be in the positive

direction or towards right and

component of

will be in the positive

direction or upwards.

The

component of

will be in the negative

direction or towards right and

component of

will be in the positive

direction or upwards.

As the

components are equal and opposite, they get cancelled. The remaining

components are equal, and both directed vertically upwards.

The net force that acts on

is therefore moving vertically upwards.

Ans:

The net force that acts on

is

.

Conclusion

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