+4q and -q are two charges separated by a distance ‘d’ metre.
Where should be a third charge +Q be
placed to attain equilibrium?
To find the position where the third charge should be placed to attain equilibrium, we need to consider the concept of electrostatic forces and balance them.
In this scenario, we have two charges:
- Charge 1: +4q
- Charge 2: -q
We need to find the position for a third charge (+Q) such that the net electrostatic force on it is zero.
Let's analyze the situation step by step:
1. Calculate the net electrostatic force on the third charge due to Charge 1 and Charge 2.
The force between two charges is given by Coulomb's law:
F = k * (|q1 * q2|) / r^2
Where:
- F is the force between the charges,
- k is the electrostatic constant (9 × 10^9 Nm^2/C^2),
- q1 and q2 are the magnitudes of the charges, and
- r is the distance between the charges.
For Charge 1 (+4q) and Charge 2 (-q), the forces are:
- Force due to Charge 1 on the third charge = k * (|(+4q) * (+Q)|) / r^2
- Force due to Charge 2 on the third charge = k * (|(-q) * (+Q)|) / r^2
2. Set up an equation to achieve equilibrium.
For the third charge to be in equilibrium, the net force on it should be zero (i.e., the forces due to Charge 1 and Charge 2 should cancel out). Thus, we equate the two forces:
k * (|(+4q) * (+Q)|) / r^2 = k * (|(-q) * (+Q)|) / r^2
Simplifying the equation:
(+4q) * (+Q) = (-q) * (+Q)
3. Solve for the position of the third charge.
To solve for the position of the third charge, we need to find the value of |(+Q)|. As the magnitudes of the charges are positive (|4q| = 4q and |-q| = q), we can cancel out |q| from both sides of the equation:
4q = -q
Simplifying the equation:
5q = 0
Dividing both sides by 5:
q = 0
If q = 0, it implies that one of the charges is zero. In this case, both Charge 1 and Charge 2 are zero. Therefore, the third charge should be placed at any position because there are no charges to exert any force on it. It will remain in equilibrium regardless of its position.
Hence, the third charge (+Q) can be placed at any position to attain equilibrium.
the charges (from left to right) ... +4q ... d ... -q ... x ... +Q
the repulsion of +4q must equal the attraction of -q
use the electrostatic force equation to find x