Two point charges Q1 and Q2 are 4C. They are 10cm apart. At what distance betwen the charges the net electric field will be zero?
At the midpoint between the charges, 5 cm from each. The E-fields due to each charge are equal and opposite there, ands cancel each other out
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To find the distance between the charges at which the net electric field is zero, we need to consider the principle of superposition.
The electric field created by each charge individually can be calculated using Coulomb's law:
Electric field created by Q1: E1 = k * |Q1| / r1^2
Electric field created by Q2: E2 = k * |Q2| / r2^2
Where:
k is the electrostatic constant (9 × 10^9 N m^2/C^2)
|Q1| and |Q2| are the magnitudes of the charges (4C in this case)
r1 and r2 are the distances from each charge to the point where you want to find the net electric field
Since the net electric field is zero, E1 = -E2 (opposite in direction but equal in magnitude) and we can set up the following equation:
E1 = -E2
k * |Q1| / r1^2 = -k * |Q2| / r2^2
Simplifying this equation, we get:
|r2|^2 / |r1|^2 = |Q2| / |Q1|
|r2|^2 / (10cm)^2 = 4C / 4C
|r2|^2 = 1
Taking the square root of both sides, we get:
|r2| = ±1
Since distances cannot be negative, we have |r2| = 1. Therefore, the distance between the charges at which the net electric field is zero is 1 cm.
To find the distance between the charges at which the net electric field is zero, we need to consider the concept of electric field due to point charges. The electric field at a point in space is a vector quantity that is created by a source charge and experienced by a test charge.
We can begin by understanding the electric field created by each point charge at a distance r from each charge using Coulomb's Law:
Electric Field (E) = k * (q / r^2)
Here, k is the electrostatic constant (k ≈ 9 × 10^9 N m^2/C^2), q is the charge, and r is the distance between the charges.
Given that Q1 and Q2 are both 4C charges and are 10cm (0.1m) apart, we can calculate the electric fields created by each charge at a given distance to find the net electric field.
Since Q1 and Q2 have equal magnitudes but opposite charges, the electric fields created by each charge will have equal magnitudes but point in opposite directions.
To cancel out the electric fields created by Q1 and Q2, the magnitudes of the electric fields should be equal. Therefore, we need to find the distance at which the electric fields created by Q1 and Q2 have equal magnitudes.
Let's assume that the distance between the charges is x. So, the electric field due to Q1 at this distance is:
E1 = k * (Q1 / x^2)
The electric field due to Q2 at the same distance is:
E2 = k * (Q2 / (0.1 - x)^2)
To achieve a net electric field of zero, the magnitudes of E1 and E2 must be equal:
|E1| = |E2|
This can be written as:
k * (Q1 / x^2) = k * (Q2 / (0.1 - x)^2)
Simplifying the equation by canceling out the k terms:
Q1 / x^2 = Q2 / (0.1 - x)^2
Substituting the values, we have:
4 / x^2 = 4 / (0.1 - x)^2
Cross-multiplying:
4 * (0.1 - x)^2 = 4 * x^2
Simplifying further:
(0.1 - x)^2 = x^2
Expanding the equation:
0.01 - 0.2x + x^2 = x^2
0.01 - 0.2x = 0
0.2x = 0.01
x = 0.01 / 0.2
x = 0.05 m
Therefore, the net electric field will be zero at a distance of 0.05 meters (5 cm) between the charges.