Two point charges q_1 = +2.40 nC and q_2 = -6.50 nC are 0.100 m apart. Point A is midway between them; point B is 0.080 m from q_1 and 0.060 m from q_2 (Fig. E23.19). Take the electric potential to be zero at infinity. Find (a) the potential at point A.

Question

Diagram showing two point charges, q1 and q2, with points A and B marked for electric potential calculations.

Accepted Answer

Hey everyone welcome back in this problem. We have an experiment with charged particles M and N. Place 65 centimeters apart. The charges are M is equal to negative 8.5 micro columns and n is equal to positive 3.5 micro columns were told that the electric potential is zero at infinity and are asked to determine the electric potential at a point between the two charges that is 30 centimeters from charge. Okay, Alright, so let's draw a quick diagram. So we have our charge em here, Okay, which is negative 8.5 Micro columns and we have our charge and over here which is 3.5 Micro Kulov's and the distance between M and N Is 65 cm. Yeah, they are 65 cm per. Now we want to have a point between the two charges that is 30 cm from em. Okay, so our point of interest it's going to be here somewhere. Okay. Where its distance to em is going to be centimeters Now, if the distance to M is 30 cm, the distance between M&N is 65 cm. Then we know that the distance between this point of interest and N must be 35 cm. Okay, alright, so we have an idea of what's going on here are a little diagram. We are asked to find the electric potential. Now let's recall the electric potential when we have more than one charge. V is equal to 1/4 by so long, not times the sum I equals one. We have two charges. So in this case we're gonna go from 1 to 2 of Q. I. The charge over ri the distance. Now this 1/4 pi E not is going to give us 9.0 times 10 to the nine. Okay. Look that table up or sorry, that number up in a table in your textbook or that your professor provided. Okay. Times. And we're going to have to multiply by this sun. Now the first element in the some let's take em to be our first charge. So we have the value of the first charge negative 8.5. Okay, we have units of cool. Um here so we want to put this into columns instead of micro columns. So we're gonna have 10 to the negative six Columns. Okay, divided by the distance to the point of interest. 30 cm which is 0.3 m. Okay then we're gonna add the information about the second charge and okay, well it has a charge of 3.5 micro cool apps. Again, putting this into columns 3.5 times 10 to the negative six columns divided by the distance for our point of interest which is 35 cm 0.35 m. Okay, Alright. Now we just need to work out this value and we will have our electric potential V So this is going to be 9. times 10 to the nine Newton meter squared per Coolum squared times -1.8 33, 3 times 10 To the - columns per meter. We're gonna get one unit of meter canceling one unit of cool and canceling. We're gonna be left with negative 165, unit Newton meter per Cool. Oh, now when we're looking at newton meter per kilo, a newton meter recall, we can write as jewel, so we get jewel per Coolum, which we remember is a volt. So our unit is actually volt here. Okay, converting this into kilovolts. Like the potential solutions we get -165 kilovolts. And that is our electric potential v. Okay. And so the answer here is going to be be the electric potential at the point of interest is negative. 165 kilovolts. Thanks everyone for watching. I hope this video helped see you in the next one.

Two point charges q_1 = +2.40 nC and q_2 = -6.50 nC are 0.100 m apart. Point A is midway between them; point B is 0.080 m from q_1 and 0.060 m from q_2 (Fig. E23.19). Take the electric potential to be zero at infinity. Find (a) the potential at point A.

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