Two point charge of +16 and -9 are placed 8cm apart in air.determine the position of the point at which the resultant electric field is zero.
24cm from right
(16/9)^1/2=d/8-d --(1)
(+,-)4/3=d/8-d
case 1 (+)
32-4d=3d
32/7=d
which is not possible as it is betweeen the two points of opposite charges resulting in repulsions
case 2 (-)
-32 +4d=3d
d=32
hence 32cm towards right
To determine the position where the resultant electric field is zero, we can use the principle of superposition. The idea is to find a point where the electric fields created by the two charges cancel each other out.
First, let's denote the two charges:
q1 = +16 (positive charge)
q2 = -9 (negative charge)
Given information:
Distance between the charges (d) = 8 cm = 0.08 m
To find the position where the resultant electric field is zero, we assume that this position is at a distance x from the positive charge (q1).
First, we need to calculate the electric field created by each charge at the position x. The electric field created by a point charge can be calculated using Coulomb's law:
Electric field created by q1 at position x (E1):
E1 = k * q1 / r1^2
where k is the electrostatic constant (k ≈ 9 × 10^9 N m²/C²), q1 is the magnitude of the charge, and r1 is the distance between q1 and the position x.
Similarly, we can calculate the electric field created by q2 at position x (E2):
E2 = k * q2 / r2^2
where q2 is the magnitude of the charge and r2 is the distance between q2 and the position x.
Since the electric fields are vectors, we consider the direction of each field. The positive charge (q1) will create an electric field pointing away from it, while the negative charge (q2) will create an electric field pointing towards it.
For the resultant electric field to be zero at the position x, the magnitudes of the electric fields created by each charge must be equal. Mathematically, this can be expressed as:
|E1| = |E2|
Squaring both sides of the equation:
(E1)^2 = (E2)^2
Substituting the expressions for E1 and E2, and simplifying, we get:
(k * q1 / r1^2)^2 = (k * q2 / r2^2)^2
Solving for r2^2, we find:
r2^2 = (q2 / q1)^2 * (r1^2)
Substituting the values:
q1 = +16
q2 = -9
r1 = x (unknown, as it represents the distance from q1 to the position x)
We can now solve for r2^2.
After finding r2, we can substitute this value back into the equation for E2 to get the electric field created by q2 at the position x. Finally, we need to equate E1 and E2 again to solve for x.
Remember that x represents the distance from the positive charge (q1) to the position where the resultant electric field is zero.
on the side of the -9 away from the +16
let d = distance from -9
16 (d + 8)^2 = 9 d^2