Two point charges 2uC and 8uC are placed 12 cm apart. Find the position of the point where electric field resultant will be zero
r is the point where they cancel
E1 = kq1/r^2
E2 = kq2/(.12-r)^2
Drop the k's set them equal and solve for r. You'll have to cross multiply and solve the quadratic.
2/x^2 = 8/(12-x)^2
1/x^2 = 4 /(12-x)^2
4 x^2 = 144 - 24 x + x^2
3 x^2 + 24 x - 144 = 0
x^2 + 8 x - 48 = 0
(x+12)(x-4) = 0
x = 4 cm
then 12 - x = 8 cm
check
2/16 = 8/64 ??? yes right
Thanks
To find the position of the point where the electric field resultant will be zero, we need to consider the concept of the superposition principle. According to the superposition principle, the electric field due to multiple point charges can be obtained by vector addition of the individual electric fields.
In this case, we have two point charges: one with a charge of 2uC and the other with a charge of 8uC. We want to find the position where the electric field resultant is zero.
Let's assume that the point where the electric field resultant is zero lies at a distance x from the 2uC charge. Therefore, the distance between the point and the 8uC charge will be 12 cm - x.
Now, we can calculate the electric field due to each charge at the given position.
For the 2uC charge:
The magnitude of the electric field due to a point charge, E1, can be calculated using Coulomb's Law:
E1 = k * q1 / r1^2,
where k is the electrostatic constant (8.99 x 10^9 N m^2/C^2), q1 is the charge of the point charge (2 x 10^-6 C), and r1 is the distance between the point charge and the position (x).
For the 8uC charge:
Similarly, E2 = k * q2 / r2^2,
where q2 is the charge of the point charge (8 x 10^-6 C) and r2 is the distance between the point charge and the position (12 cm - x).
Since we want the resultant electric field to be zero, the vectors E1 and E2 should cancel each other out, i.e.,
E1 + E2 = 0.
Now, we can substitute the values and solve the equation for x.
k * q1 / r1^2 + k * q2 / r2^2 = 0.
Substituting the respective values, we get:
(8.99 x 10^9 N m^2/C^2) * (2 x 10^-6 C) / x^2 + (8.99 x 10^9 N m^2/C^2) * (8 x 10^-6 C) / (12 cm - x)^2 = 0.
Simplifying the equation and solving for x will give us the position of the point where the electric field resultant is zero.