The main concept used to solve the problem is electric potential due to a point charge.
Initially, Calculate the distance of the charges on the corners of the square from the center using Pythagoras theorem.
Finally, calculate the magnitude and direction of electric potential using the relation equating electric potential with charge and distance.
The electric potential is a quantity numerically equal to the potential energy of a unit positive charge at a given point of the field. The formula for electric potential is,
Here, is coulomb’s constant, is the charge and is the distance.
The figure given below shows the arrangement of charges around the square.
Here, is the charge and d is the distance.
From the figure given above,
In triangle XAW,
Substitute for and in the above equation.
Also,
The electric potential at point P due to the charge placed at the corner of the square A is,
Here, is the coulomb’s constant, is the charge at point A and is the distance of point A from point P.
Substitute for and for in the above equation.
The electric potential at point P due to the charge placed at the corner of the square B is,
Here, is the coulomb’s constant, is the charge at point B and is the distance of point B from point P.
Substitute for and for in the above equation.
The electric potential at point P due to the charge placed at the corner of the square C is,
Here, is the coulomb’s constant, is the charge at point C and is the distance of point C from point P.
Substitute for and for in the above equation.
The electric potential at point P due to the charge placed at the corner of the square D is,
Here, is the coulomb’s constant, is the charge at point D and is the distance of point D form point P.
Substitute for and for in the above equation.
From the figure given above,
The electric potential at point P due to the charge placed at point X is,
Here, is the coulomb’s constant, is the charge at point X and is the distance of point X from point P.
Substitute for and for in the above equation.
The electric potential at point P due to the charge placed at point Y is,
Here, is the coulomb’s constant, is the charge at point Y and is the distance of point Y from point P.
Substitute for and for in the above equation.
The electric potential at point P due to the charge placed at point Z is,
Here, is the coulomb’s constant, is the charge at point C and is the distance of point Z from point P.
Substitute for and for in the above equation.
The electric potential at point P due to the charge placed at point W is,
Here, is the coulomb’s constant, is the charge at point W and is the distance of point W form point P.
Substitute for and for in the above equation.
The total potential at point P due to all the charges is,
Substitute for , for , for , for , for , for , for and for in the above equation.
…… (1)
Also, the coulomb’s constant is given by,
Substitute for in equation (1).
Ans:
The electric potential at point P is .
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