Question

Two small spheres with charges q1 = +9 nC and q2 = -3 nC are placed at marks x1 = -2 cm and x2 = 13 cm. Where along the x-axis should you place a third sphere with charge q3 so that the sum of the forces exerted by the first two spheres on the third one is zero?

Answer 1

To find the position along the x-axis where the sum of the forces exerted by the first two spheres on the third one is zero, we can use Coulomb's law. The forces between the charges are given by F = k * (|q1*q2| / r^2). By setting the forces equal to zero and solving for x, we can determine the desired position.

Step-by-step explanation:

To find the location along the x-axis where a third sphere with charge q3 should be placed so that the sum of the forces exerted by the first two spheres on the third one is zero, we need to consider the forces between the charges. According to Coulomb's law, the force between two point charges is given by:

F = k * (|q1*q2| / r^2)

Where k is the Coulomb's constant, q1 and q2 are the charges of the two spheres, and r is the distance between them. In this case, the force exerted by q1 on q3 is:

F1 = k * (|q1*q3| / (x - x1)^2)

And the force exerted by q2 on q3 is:

F2 = k * (|q2*q3| / (x - x2)^2)

For the sum of the forces to be zero, we must have:

F1 + F2 = 0

Substituting the values of q1, q2, x1, and x2, we can solve for x to find the position where the sum of the forces is zero.

Here, a=2, b=−82, and

c=437. Plug these values into the formula to find x_{3} . You should find two possible positions for x_{3}

Answer 2

Step-by-step explanation:

Given

Charge on particles

`q_1=+9\ nC`

`q_2=-3\ nC`

`x_1=-2\ cm`

`x_2=13\ cm`

Third charge
`q_3` must be placed right side of
`q_2` as
`q_2` will attract and
`q_1 will repel the [tex]q_3` so net force will be zero

Electrostatic force is given by

`F=(kq_1q_2)/(r^2)`

suppose
`q_3` is at a distance of x cm from
`q_2`

`F_(13)=(kq_1q_3)/((13+2+x)^2)`

`F_(23)=(kq_2q_3)/((x)^2)`

`F_(13)+F_(23)=0`

`(k(9)(q_3))/((15+x)^2)=(k3q_3)/((x)^2)`

`x(√(3)-1)=15`

`x=(15)/(√(3)-1)`

`x=20.49\ cm`