Question

A point of charge 4.9 μC is placed at the origin (x1 = 0) of a coordinate system, and another charge of -1.1 μC is placed on the x-axis at x2 = 0.28 m. a) Where on the x-axis can a third charge be placed in meters so that the net force on it is zero?

b) What if both charges are positive; that is, what if the second charge is 1.9 μC?

Answer 1

To find the location on the x-axis where a third charge can be placed so that the net force on it is zero, we need to consider the forces exerted by the two charges. If both charges are positive, the net force on a third charge placed on the x-axis will never be zero.

Step-by-step explanation:

a) To find the location on the x-axis where a third charge can be placed so that the net force on it is zero, we need to consider the forces exerted by the two charges. The net force will be zero when the two forces are equal in magnitude but opposite in direction. Using Coulomb's law, we can calculate the force between the first charge and the third charge at an unknown position x3. We can then set that force equal to the force between the second charge and the third charge at the same position x3, and solve for x3.

b) If both charges are positive, the net force on a third charge placed on the x-axis will never be zero. Positive charges repel each other, so the forces will always be in the same direction.

Answer 2

a)The third charge is placed at a distance of r=0.253 m from the charge of
`-1.1\ \rm \mu C` on right side of it

b) The third charge is placed at a distance of r=0.1762 m from the charge of magnitude
`4.9\ \rm \mu C` on its right side on x axis.

Step-by-step explanation:

Given:

• Charge of magnitude
  `4.9\ \rm \mu C` is placed at origin.
• Charge of magnitude
  `-1.1\ \rm \mu C` placed at x=0.28 m

a)Let the The third charge is placed at a distance of r m from the charge of
`-1.1\ \rm \mu C` on right side of it. When one charge is positive and other charge is negative and net force on third charge is zero

`(4.9* Q)/(4\pi \epsilon_0(r+0.28)^2)=(1.1* Q)/(4\pi \epsilon_0r^2)\\\\r=0.245\ \rm m`

b) If both charges are positive

Let The third charge is placed at a distance of r from the charge of magnitude
`4.9\ \rm \mu C` on its right side on x axis. then

`(4.9* Q)/(4\pi \epsilon_0(r)^2)=(1.9* Q)/(4\pi \epsilon_0(0.28-r)^2)\\\\r=0.1726\ \rm m`