To find the point at which the electric field vector is zero, we can use the principle that the electric field due to two point charges is given by the vector sum of the electric fields due to each individual charge.
First, let's denote the position of the first object with charge -1.50 C as Q1, and the position of the second object with charge +6.85 C as Q2.
Next, let's consider a point P at which we want the electric field vector to be zero.
The electric field due to Q1 at point P is given by the formula:
E1 = (k * |Q1|) / (r1^2)
Where k is the electrostatic constant (approximately 9 x 10^9 N m^2/C^2), |Q1| is the magnitude of the charge of Q1 (1.50 C) and r1 is the distance from Q1 to point P.
Similarly, the electric field due to Q2 at point P is given by:
E2 = (k * |Q2|) / (r2^2)
Where |Q2| is the magnitude of the charge of Q2 (6.85 C) and r2 is the distance from Q2 to point P.
Since we want the electric field vector to be zero at point P, the vector sum of E1 and E2 should be zero:
E1 + E2 = 0
Substituting the expressions for E1 and E2, we have:
(k * |Q1|) / (r1^2) + (k * |Q2|) / (r2^2) = 0
Simplifying this equation, we get:
(|Q1| / r1^2) + (|Q2| / r2^2) = 0
Now, we can rearrange this equation to solve for r2^2:
(|Q2| / r2^2) = - (|Q1| / r1^2)
r2^2 / |Q2| = -r1^2 / |Q1|
Taking the square root of both sides:
r2 / sqrt(|Q2|) = -r1 / sqrt(|Q1|)
To find the point at which the electric field vector is zero, we need to find the ratio of the distances from the charges to that point:
r2 / r1 = - sqrt(|Q2|) / sqrt(|Q1|)
Plugging in the given values:
r2 / 2.00m = - sqrt(6.85 C) / sqrt(1.50 C)
Simplifying this equation gives us the ratio of distances:
r2 / 2.00m = -1.98
Finally, we can solve for r2 by multiplying both sides by 2.00m:
r2 = -3.96m
Therefore, the electric field vector will be zero at a point that is -3.96m away from the second charge, Q2.
Two point charges are 2.00 m apart as shown on the right. The charge of the first object is -1.50 C, while the second object has a charge of +6.85 C. At which point will the electric field vector be zero?
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