Four identical charges Q are placed at the corners of a square of side L.
1.Find the magnitude total force exerted on one charge by the other
three charges.
|F| = ?
The concepts that are required to solve this problem are electric force between two point charges, resolution of a vector in to rectangular components, and the net force on an object due to multiple forces acting on it simultaneously.
Initially, call four identical point charges as A, B, C, and D. Place the four charges at four corners of a square of side length L in clockwise order. Later, calculate the electric force on the charge B due to charges A, C, and D in vector form. Later, add these three forces on charge B in vector form. This force vector is called net force vector on the charge B due to other three charges. Later, calculate the magnitude of this force vector.
The magnitude of the electric force F on a charge due to other charge can be calculated using the following formula:
Here, k is the Coulomb’s constant and r is the distance between the two charges.
From the super position principle, the net electric force on a charge B due to other three charges A, C, and D is equal to the vector sum of the electric force on the charge B due to these three charges.
Here, is the vector form of electric force on charge B due to charge A, is the vector form of electric force on charge B due to charge C, and is the vector form of electric force on charge B due to charge D.
From the Pythagoras theorem, in a right angle triangle, the square of the hypotenuse is equal to the sum of the square of each side of the triangle.
Magnitude of a two dimensional vector can be calculated using the following formula:
Here, is the x-component of the vector and is the y-component of the vector.
The figure given below represents the arrangement of four charges at corners of a square and the direction of all the electric forces acting on a charge due to other three charges:
Substitute Q for and , L for r in the equation , and calculate the magnitude of the force on charge B due to charge A.
The vector form of the force on charge B due to charge A is,
Substitute Q for and , L for r in the equation , and calculate the magnitude of the force on charge B due to charge C.
The vector form of the force on charge B due to charge C is,
Substitute Q for and , for r in the equation , and calculate the magnitude of the force on charge B due to charge D.
The vector form of the force on charge B due to charge D is,
Substitute for and for , and for in the equation .
The magnitude of the vector is,
Ans:
The magnitude of the net force acting on a charge due to other three charges when four identical charges are placed at four corners of a square is .
Four identical charges Q are placed at the corners of a square of side L.
PRACTICE: Four identical point charges, q, are placed at the corners of a square. Each side of the square has length L. What is the magnitude of the electric field at the point P, the center of the square? A) O B) kq</L2 C) kq7I2L2 D) kq2/4L2
Four charges are placed at the corners of a square, where q is positive (q > 0). Initially there is no charge in the center of the square. a) Find the work W required to bring the charge Qf = +q from infinity and place it at the center of the square. b) What is the magnitude of the electric force on the charge q when it is placed at the center of the square? c) What is the magnitude...
Four identical charged particles (q = +10.9 µC) are located on the corners of a rectangle as shown in the figure below. The dimensions of the rectangle are L = 57.0 cm and W = 13.5 cm.(a) Calculate the magnitude of the total electric force exerted on the charge at the lower left corner by the other three charges.(b) Calculate the direction of the total electric force exerted on the charge at the lower left corner by the other three...
A charge Q is placed at the center of the square of side 8.3cm, at the corners of which four identical charges q=7.5C are placed. Find the value of the charge Q so that the system is at equilibrium. Problem3 A charge Q is placed at the centre of the square of side 8.30 cm, at the corners of which four identical charges q 75 C are placed. Find the value of the charge Q so that the whole system...
Identical point charges q-15.00μC are placed at opposite corners of a square. The length of each side of the square is 0.200 m. A point charge q0--200μC is placed at one of the empty corners. Part A How much work is done on qo by the electric force when go is moved to the other empty corner? Express your answer using one significant figure. Submit Request Answer
Three charges, each of magnitude 3 nC, are at the corners of a square of side 5 cm. The two charges at the opposite corners are positive and the other is negative. Find the force exerted by these charges on a fourth charge q = 3 nC at the remaining corner.
heeeeeeelppp Identical point charges Q are placed at each of the four corners of a 1.0 m times 2.0 m rectangle. If the magnitude of the electrostatic force on one of the charges is 28.5 N, what is the charge, Q of one of the four charges? mu C
Three identical point charges (q = 1.6 times 10^-19 C) are placed at each of three corners of a square of side L and cannot move. A) Draw the free body diagram for a charge of -3q placed at the center of the square labeling all the forces acting on the charge -3q B) Calculate the magnitude and direction of the force on the -3q charge Three identical point charges (q = 1.6 times 10^-19 C) are placed at each...
each side. Find 5. Four point-like charges are placed as shown in the figure, three of them are at the corners and one at the center of a square, 40.0 cm on the magnitude o the net electrostatic force exerted on the point charge gu.Let q +160 C,220 pC, and q, -49.0pc. 42 as q1
Four identical charged particles (q = +10.8 µC) are located on the corners of a rectangle as shown in the figure below. The dimensions of the rectangle are L = 57.0 cm and W = 14.1 cm. (a) Calculate the magnitude of the total electric force exerted on the charge at the lower left corner by the other three charges. (b) Calculate the direction of the total electric force exerted on the charge at the lower left corner by the...