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"A point charge Q is located at the point A(x,y,z) in space. The force acting on a test charge q located at the point B(x + dx, y + dy, z + dz) is given by Coulomb's law asF = (kqQ)/(r^2) * r̂ where k is the Coulomb constant, r̂ is the unit vector in the direction of the vector r = (x + dx - x, y + dy - y, z + dz - z), and r = |r|. Using the principle of superposition of forces, show that the force on the test charge at B due to the charges at A and at B isF'?
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"A point charge Q is located at the point A(x,y,z) in space. The force...
Superposition of Forces

The principle of superposition of forces states that the total force acting on a charge due to multiple charges is equal to the vector sum of the individual forces acting on that charge due to each individual charge.

Force due to Charge A

Let's consider the force acting on the test charge q at point B due to the charge Q at point A. According to Coulomb's law, the force is given by:

F₁ = (kqQ)/(r₁^2) * r̂₁

Here, r₁ is the distance between points A and B, and r̂₁ is the unit vector in the direction from A to B.

Force due to Charge B

Similarly, the force acting on the test charge q at point B due to the charge Q at point B itself can be given by:

F₂ = (kqQ)/(r₂^2) * r̂₂

Here, r₂ is the distance between points B and B (which is zero), and r̂₂ is the unit vector in the direction from B to B (zero vector).

Total Force

To find the total force on the test charge q at point B, we need to sum up the individual forces due to charges A and B.

F' = F₁ + F₂

Since r₂ = 0, the second term F₂ becomes zero. Therefore, the total force can be simplified as:

F' = F₁

Calculating F₁

Now, let's calculate the force F₁ due to charge A at point B. We can express r₁ as a vector:

r₁ = (x + dx - x)î + (y + dy - y)ĵ + (z + dz - z)k̂

Simplifying this:

r₁ = dxî + dyĵ + dzk̂

The magnitude of r₁ is given by:

|r₁| = √(dx^2 + dy^2 + dz^2)

Substituting the values into the expression for F₁, we get:

F₁ = (kqQ)/(r₁^2) * r̂₁

F₁ = (kqQ)/(dx^2 + dy^2 + dz^2) * (dxî + dyĵ + dzk̂)

Therefore, the force on the test charge q at point B due to the charges at points A and B is given by F₁.
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"A point charge Q is located at the point A(x,y,z) in space. The force acting on a test charge q located at the point B(x + dx, y + dy, z + dz) is given by Coulomb's law asF = (kqQ)/(r^2) * r̂ where k is the Coulomb constant, r̂ is the unit vector in the direction of the vector r = (x + dx - x, y + dy - y, z + dz - z), and r = |r|. Using the principle of superposition of forces, show that the force on the test charge at B due to the charges at A and at B isF'?
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"A point charge Q is located at the point A(x,y,z) in space. The force acting on a test charge q located at the point B(x + dx, y + dy, z + dz) is given by Coulomb's law asF = (kqQ)/(r^2) * r̂ where k is the Coulomb constant, r̂ is the unit vector in the direction of the vector r = (x + dx - x, y + dy - y, z + dz - z), and r = |r|. Using the principle of superposition of forces, show that the force on the test charge at B due to the charges at A and at B isF'? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about "A point charge Q is located at the point A(x,y,z) in space. The force acting on a test charge q located at the point B(x + dx, y + dy, z + dz) is given by Coulomb's law asF = (kqQ)/(r^2) * r̂ where k is the Coulomb constant, r̂ is the unit vector in the direction of the vector r = (x + dx - x, y + dy - y, z + dz - z), and r = |r|. Using the principle of superposition of forces, show that the force on the test charge at B due to the charges at A and at B isF'? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for "A point charge Q is located at the point A(x,y,z) in space. The force acting on a test charge q located at the point B(x + dx, y + dy, z + dz) is given by Coulomb's law asF = (kqQ)/(r^2) * r̂ where k is the Coulomb constant, r̂ is the unit vector in the direction of the vector r = (x + dx - x, y + dy - y, z + dz - z), and r = |r|. Using the principle of superposition of forces, show that the force on the test charge at B due to the charges at A and at B isF'?.
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Here you can find the meaning of "A point charge Q is located at the point A(x,y,z) in space. The force acting on a test charge q located at the point B(x + dx, y + dy, z + dz) is given by Coulomb's law asF = (kqQ)/(r^2) * r̂ where k is the Coulomb constant, r̂ is the unit vector in the direction of the vector r = (x + dx - x, y + dy - y, z + dz - z), and r = |r|. Using the principle of superposition of forces, show that the force on the test charge at B due to the charges at A and at B isF'? defined & explained in the simplest way possible. Besides giving the explanation of "A point charge Q is located at the point A(x,y,z) in space. The force acting on a test charge q located at the point B(x + dx, y + dy, z + dz) is given by Coulomb's law asF = (kqQ)/(r^2) * r̂ where k is the Coulomb constant, r̂ is the unit vector in the direction of the vector r = (x + dx - x, y + dy - y, z + dz - z), and r = |r|. Using the principle of superposition of forces, show that the force on the test charge at B due to the charges at A and at B isF'?, a detailed solution for "A point charge Q is located at the point A(x,y,z) in space. The force acting on a test charge q located at the point B(x + dx, y + dy, z + dz) is given by Coulomb's law asF = (kqQ)/(r^2) * r̂ where k is the Coulomb constant, r̂ is the unit vector in the direction of the vector r = (x + dx - x, y + dy - y, z + dz - z), and r = |r|. Using the principle of superposition of forces, show that the force on the test charge at B due to the charges at A and at B isF'? has been provided alongside types of "A point charge Q is located at the point A(x,y,z) in space. The force acting on a test charge q located at the point B(x + dx, y + dy, z + dz) is given by Coulomb's law asF = (kqQ)/(r^2) * r̂ where k is the Coulomb constant, r̂ is the unit vector in the direction of the vector r = (x + dx - x, y + dy - y, z + dz - z), and r = |r|. Using the principle of superposition of forces, show that the force on the test charge at B due to the charges at A and at B isF'? theory, EduRev gives you an ample number of questions to practice "A point charge Q is located at the point A(x,y,z) in space. The force acting on a test charge q located at the point B(x + dx, y + dy, z + dz) is given by Coulomb's law asF = (kqQ)/(r^2) * r̂ where k is the Coulomb constant, r̂ is the unit vector in the direction of the vector r = (x + dx - x, y + dy - y, z + dz - z), and r = |r|. Using the principle of superposition of forces, show that the force on the test charge at B due to the charges at A and at B isF'? tests, examples and also practice JEE tests.
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