two points of charge values Q and q are placed of x and x/2 respectively from third charge of value 4q, all charges being in the same straight line. calculate the magnitude and nature of charge Q such that the net force experienced by the charge q is zero?
4q
To calculate the magnitude and nature of charge Q such that the net force experienced by the charge q is zero, we need to use the principle of electrostatic force and apply Newton's Third Law.
Let's break down the problem step by step:
1. Assume that the charge q experiences a net force of zero due to the charges Q and 4q.
2. According to Coulomb's Law, the electrostatic force between two charges is given by:
F = k * (|Q| * |q|) / r^2
Where F is the force, k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2), |Q| and |q| are the magnitudes of charges Q and q respectively, and r is the distance between the charges.
3. The net force on q is zero, which means that the forces due to Q and 4q must be equal in magnitude but opposite in direction. We can express this as:
F(Q on q) = -F(4q on q)
4. We can then substitute the expressions for each force:
k * (|Q| * |q|) / x^2 = -k * (|4q| * |q|) / (x/2)^2
Simplifying, we get:
|Q| / x^2 = -|4q| / (x/2)^2
|Q| / x^2 = -16 * |q| / x^2
5. Since the magnitudes of charges cannot be negative, we can simplify further by removing the absolute value signs:
|Q| = -16 * |q|
Therefore, the magnitude of charge Q is 16 times the magnitude of charge q.
6. Since we want the net force to be zero, charges of equal magnitude but opposite signs would satisfy this requirement. Thus, the nature of charge Q should be opposite to that of charge q.
In summary, the magnitude of charge Q should be 16 times the magnitude of charge q, and the nature of charge Q should be opposite to the nature of charge q.