Two point charges, Q1𝑄1 = 3.0 μC𝜇C and Q2𝑄2 = -1.9 μC𝜇C , are placed on the x𝑥 axis. Suppose that Q2𝑄2 is placed at the origin, and Q1𝑄1 is placed at the coordinate x1𝑥1 = −− 6.0 cmcm (Figure 1).Figure1 of 1Part APart completeAt what point(s) along the x𝑥 axis is the electric field zero? Determine the x𝑥 -coordinate(s) of the point(s).Express your answer using two significant figures. If there is more than one answer, enter your answers in ascending order separated by commas.xE𝑥𝐸 =23 cmcm SubmitPrevious Answers CorrectTerm 1: Correct answer is shown. Your answer 23.3423.34 cmcm was either rounded differently or used a different number of significant figures than required for this part.Part BAt what point(s) along the x𝑥 axis is the potential zero? Determine the x𝑥 -coordinate(s) of the point(s).Express your answer using two significant figures. If there is more than one answer, enter your answers in ascending order separated by commas.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typexV𝑥𝑉 =10.36,0cmcm
Question
Two point charges, Q1𝑄1 = 3.0 μC𝜇C and Q2𝑄2 = -1.9 μC𝜇C , are placed on the x𝑥 axis. Suppose that Q2𝑄2 is placed at the origin, and Q1𝑄1 is placed at the coordinate x1𝑥1 = −− 6.0 cmcm (Figure 1).Figure1 of 1Part APart completeAt what point(s) along the x𝑥 axis is the electric field zero? Determine the x𝑥 -coordinate(s) of the point(s).Express your answer using two significant figures. If there is more than one answer, enter your answers in ascending order separated by commas.xE𝑥𝐸 =23 cmcm SubmitPrevious Answers CorrectTerm 1: Correct answer is shown. Your answer 23.3423.34 cmcm was either rounded differently or used a different number of significant figures than required for this part.Part BAt what point(s) along the x𝑥 axis is the potential zero? Determine the x𝑥 -coordinate(s) of the point(s).Express your answer using two significant figures. If there is more than one answer, enter your answers in ascending order separated by commas.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typexV𝑥𝑉 =10.36,0cmcm
Solution
The electric field is zero at the point along the x-axis where the forces exerted by the two charges on a test charge cancel each other out. This can occur at two points: one between the charges and one on the side of the charge with the larger magnitude.
The electric field E due to a point charge Q at a distance r from the charge is given by Coulomb's law:
E = kQ/r^2
where k is Coulomb's constant.
Setting the electric fields due to the two charges equal to each other gives:
kQ1/r1^2 = kQ2/r2^2
Solving this equation for r (the distance from the origin) gives the points where the electric field is zero.
The potential V at a point due to a point charge Q at a distance r from the point is given by:
V = kQ/r
The potential is zero at the point along the x-axis where the potentials due to the two charges add up to zero. This can only occur between the two charges.
Setting the potentials due to the two charges equal to each other gives:
kQ1/r1 = kQ2/r2
Solving this equation for r gives the point where the potential is zero.
So, the electric field is zero at x = 23 cm and the potential is zero at x = 10.36 cm and x = 0 cm.
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