2 spheres of radii 10cm and 20cm contains charges 10microcoulomb and 20 micro coulomb respectively.they are separated by a distance 100cm.Where will the electric field be zero?
To find the point where the electric field is zero, we need to consider the concept of the Electric Field due to point charges.
The electric field due to a point charge is given by:
E = k * (Q / r^2)
where E is the electric field, Q is the charge, r is the distance between the charge and the point where we want to calculate the field, and k is the electrostatic constant (k = 9 × 10^9 N m^2/C^2).
In this case, we have two spheres with charges Q1 = 10 microcoulomb and Q2 = 20 microcoulomb, and we need to find where the electric field due to these charges is zero.
Let's assume that the center of the smaller sphere is at the origin (0, 0, 0), and the center of the larger sphere is at (100 cm, 0, 0). We need to find the position where the electric field due to both spheres is zero.
To find this position, we can set up two equations based on the electric field due to each sphere:
E1 = k * (Q1 / r1^2)
E2 = k * (Q2 / r2^2)
where r1 is the distance between the point and the center of the smaller sphere and r2 is the distance between the point and the center of the larger sphere.
Since the electric field is zero at the point we are looking for, we can set E1 = -E2 (as they have opposite directions). This gives us:
k * (Q1 / r1^2) = -k * (Q2 / r2^2)
Simplifying the equation, we get:
Q1 / r1^2 = -Q2 / r2^2
Plugging in the given values, we have:
(10 * 10^-6 C) / r1^2 = -(20 * 10^-6 C) / r2^2
Solving for r1^2 and r2^2, we find:
r1^2 = -(2 * r2^2)
r1 = sqrt(2) * r2
Since the r1 and r2 are distances, they must be positive. Thus, we can express the position where the electric field is zero as:
r1 = sqrt(2) * r2
Now, substituting the given distance (100 cm) for r2:
r1 = sqrt(2) * 100 cm
r1 = 100 * sqrt(2) cm
Hence, the electric field will be zero at a position (100 * sqrt(2) cm, 0, 0) or approximately (141.42 cm, 0, 0).