2 charge of 10 microcoulomb and 40 microcoulomb respectively 12cm apart find the position of a point where electric field is zero

To find the position where the electric field is zero due to two charges, you can use the principle of superposition. According to this principle, the electric field at any point is the vector sum of the electric fields due to each individual charge.

Let's denote the charges as Q1 and Q2, with magnitudes of 10 μC and 40 μC, respectively. They are placed 12 cm apart.

To find the position where the electric field is zero, you need to find a point between the charges where the electric field due to charge Q1 is equal in magnitude but opposite in direction to the electric field due to charge Q2.

Mathematically, you can write the electric field due to each charge as:

Electric field due to Q1, E1 = k * Q1 / r1^2
Electric field due to Q2, E2 = k * Q2 / r2^2

Where:
k is Coulomb's constant (k = 9 x 10^9 Nm^2/C^2)
Q1 and Q2 are the magnitudes of the charges
r1 and r2 are the distances between the point and each charge

Since we want the electric field to be zero, we can set E1 = -E2.

k * Q1 / r1^2 = -k * Q2 / r2^2

Now, substitute the values given:

(9 x 10^9 Nm^2/C^2) * (10 x 10^-6 C) / r1^2 = -(9 x 10^9 Nm^2/C^2) * (40 x 10^-6 C) / r2^2

Simplifying the equation, we have:

r2^2 / r1^2 = 4

Taking the square root of both sides gives:

r2 / r1 = 2

Since the ratio of the distances is 2, we can say that r2 is twice the distance from the point to charge Q1. Therefore, the point where the electric field is zero is located twice as far from charge Q1 as it is from charge Q2.

To find the actual position, you can determine the distance of the point from charge Q1, which is r1. Then, multiply r1 by 2 to get r2.

To summarize, the position where the electric field is zero is located at a distance r1 from charge Q1, and at twice that distance (2 * r1) from charge Q2.

Solution