Question

What is (Fnet3)x, the x-component of the net force exerted by these two charges on a third charge q3 = 55.0 nC placed between q1 and q2 at x3 = -1.220 m ? Your answer may be positive or negative, depending on the direction of the force. Express your answer numerically in newtons to three significant figures.

Answer 1

Complete Question

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The rest of the question

What is (Fnet3)x, the x-component of the net force exerted by these two charges on a third charge q3 = 55.0 nC placed between q1 and q2 at x3 = -1.220 m ? Your answer may be positive or negative, depending on the direction of the force. Express your answer numerically in newtons to three significant figures.

Answer:

The net force exerted on the third charge is
`F_(net)= 3.22*10^(-5) \ J`

Step-by-step explanation:

From the question we are told that

The third charge is
`q_3 = 55 nC = 55 *10^(-9) C`

The position of the third charge is
`x = -1.220 \ m`

The first charge is
`q_1 = -16 nC = -16 *10^(-9) \ C`

The position of the first charge is
`x_1 = -1.650m`

The second charge is
`q_2 = 32 nC = 32 *10^(-9) C`

The position of the second charge is
`x_2 = 0 \ m`

The distance between the first and the third charge is

`d_(1-3) = -1.650 -(-1.220)`

`d_(1-3) = -0.43 \ m`

The force exerted on the third charge by the first is

`F_(1-3) = (k q_1 q_3)/(d_(1-3)^2)`

Where k is the coulomb's constant with a value
`9*10^(9) \ kg\cdot m^3\cdot s^(-4)\cdot A^2.`

substituting values

`F_(1-3) = (9*10^(9)* 16 *10^(-9) * (55*10^(-9)))/((-0.43)^2)`

`F_(1-3) = 4.28 *10^(-5) \ N`

The distance between the second and the third charge is

`d_(2-3) = 0- (-1.22)`

`d_(2-3) =1.220 \ m`

The force exerted on the third charge by the first is mathematically evaluated as

`F_(2-3) = (k q_2 q_3)/(d_(2-3)^2)`

substituting values

`F_(2-3) = (9*10^(9) * (32*10^(-9)) *(55*10^(-9)))/((1.220)^2)`

`F_(2-3) = 1.06*10^(-5) N`

The net force is

`F_(net) = F_(1-3) -F_(2-3)`

substituting values

`F_(net) = 4.28 *10^(-5) - 1.06*10^(-5)`

`F_(net)= 3.22*10^(-5) \ J`