A positive point charge Q is located at x=a and a negative point charge −Q is at x=−a. A positive charge q can be placed anywhere on the y-axis.
1) Find an expression for (Fnet)x, the x-component of the net force on q. (Give your answer in terms of Q, q, a, y and constant K.)
The concept required to solve the given problem is electrostatic force between two charges.
Calculate the electrostatic force due to the charges on by using expression for electrostatic force. Then, take the vector sum of these forces to fine the net force on the charge q.
According to Coulomb’s law, the force of attraction or repulsion between two charged particles is proportional to product magnitude of charge on each particle and inversely proportional to square of the distance between the charges.
The electrostatic force between two charges is given as follows:
Here, is the coulomb’s constant, are the charges and is the distance between two charges .
Draw the following figure from given data.
From the figure, distance between charges q and Q can be calculated by using Pythagoras theorem as,
From the figure, distance between charges q and -Q can be calculated by using Pythagoras theorem as,
From the figure, the vector form of electrostatic force on charge q due to charge Q is given as follows:
From the figure, the vector form of electrostatic force on charge q due to charge -Q is given as follows:
The net force F on q is equal to the sum of forces and
Substitute for and for in the above equation.
Substitute for and in the above equation.
From the figure, the values of is,
Substitute for in the above equation and solve for F.
Ans:
The x-component of force on the charge q is
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