You are given two unknown point charges, Q1 and Q2. At a point on the line joining them, one-third of the way from Q1 to Q2 the electric field is zero . What is the ratio Q1/Q2?
E is directly proportional to q
Break the distance into three parts, one between q1,Q2, and the other two parts on the Q2 side.
q1/1^2=q2/2^2
q1/q2=1/4
Well, it sounds like Q1 and Q2 are having a field day, quite literally! One-third of the way and bam, zero electric field! I'm guessing they're playing a fun game of hide and seek with the charges.
But to answer your question, I need to use my "Charger's Manual" here. Let's see... Ah, page 42: "The electric field at a point on the line joining two point charges is zero when the distance from the first charge to the point is equal to the ratio of the second charge to the total sum of the charges."
So, using that formula, we have:
(Q1 / (1/3)) = (Q2 / (1 - 1/3))
Simplifying that equation, we get:
3Q1 = 2Q2
So, the ratio of Q1 to Q2 is 3:2, or if you prefer, the game they're playing is the "Hide-and-Seek: Electric Edition," where Q1 is the seeker and Q2 is the hider, with Q1 having a three times greater charge. Good luck to both charges, may the electric field be ever in their favor!
To solve this problem, we can use the concept of electric field due to point charges.
Step 1: Let's assume that the distance between the two charges, Q1 and Q2, is given by d.
Step 2: We are given that at a point on the line joining the charges, one-third of the way from Q1 to Q2, the electric field is zero. This means that the electric field due to Q1 cancels out the electric field due to Q2 at this point.
Step 3: The electric field due to a point charge at any given point depends on the distance from the charge. The electric field due to a point charge, Q, at a distance, r, is given by Coulomb's Law:
E = k * Q / r^2,
where E is the electric field, k is the electrostatic constant, Q is the charge, and r is the distance from the point charge.
Step 4: Since the electric field is zero at a point one-third of the way from Q1 to Q2, we can set up the following equation:
E1 + E2 = 0,
where E1 is the electric field due to Q1 and E2 is the electric field due to Q2 at this point.
Step 5: Let's calculate the distances of this point from Q1 and Q2. Since it is one-third of the way from Q1 to Q2, it is located at (1/3)d from Q1 and (2/3)d from Q2.
Step 6: Now, using the equation from Step 3 and the distances calculated in Step 5, we can express the electric fields due to Q1 and Q2 as follows:
E1 = k * Q1 / (1/3d)^2,
E2 = k * Q2 / (2/3d)^2.
Step 7: Substituting the expressions for E1 and E2 into the equation from Step 4, we get:
k * Q1 / (1/3d)^2 + k * Q2 / (2/3d)^2 = 0.
Step 8: Simplifying the equation in Step 7, we have:
Q1 / (1/9d^2) + Q2 / (4/9d^2) = 0.
Step 9: Multiplying through by (9d^2) to clear the denominators, we get:
9Q1 + 4Q2 = 0.
Step 10: Dividing both sides of the equation by Q2, we obtain:
Q1 / Q2 = -4 / 9.
Therefore, the ratio Q1/Q2 is -4/9.
To solve this problem, we can use the concept of electric field due to point charges. The electric field at a point due to a point charge Q can be calculated using the formula:
E = k * Q / r^2
where E is the electric field, k is the electrostatic constant (9 × 10^9 Nm^2/C^2), Q is the charge, and r is the distance from the point charge.
Now, let's analyze the situation given in the problem. We have two point charges, Q1 and Q2, and we are given that at a point on the line joining them, one-third of the way from Q1 to Q2, the electric field is zero. Let's denote the distance between Q1 and Q2 as d.
At this point, the electric field is zero, so we can set up the following equation:
E1 + E2 = 0
Using the formula for electric field, we can substitute the values:
(k * Q1 / (d/3)^2) + (k * Q2 / (2d/3)^2) = 0
Simplifying this equation, we get:
Q1 / (1/9) + Q2 / (4/9) = 0
9 * Q1 + 4 * Q2 = 0.
Now, we have two unknowns and one equation. To find Q1/Q2, we need another equation. If there is an additional piece of information or equation available, you can use that to solve for the ratio of the charges. Otherwise, based on the given information alone, it is not possible to determine the ratio Q1/Q2.