NEET Exam > NEET Questions > A charge -q1 is kept at a distance y from the...
Start Learning for Free
A charge -q1 is kept at a distance y from the origin on Y-axis and another charge -q2 is kept at a distance x from the origin on X-axis. The value of x for the x-component of the force on q1 to be maximum is1) x = y/22) x =y/√23) x= y4) x= √2y
Most Upvoted Answer
A charge -q1 is kept at a distance y from the origin on Y-axis and ano...
Problem: Find the value of x for the x-component of the force on q1 to be maximum when a charge -q1 is kept at a distance y from the origin on Y-axis and another charge -q2 is kept at a distance x from the origin on X-axis.
Solution:
To find the value of x for the x-component of the force on q1 to be maximum, we need to find the expression for the force acting on q1, and then differentiate it with respect to x to find the value of x that maximizes the force.
Let us consider the charges -q1 and -q2 at their respective positions as shown in the figure below:
From Coulomb's law, the force F1 on charge q1 due to charge q2 is given by:
F1 = kq1q2 / r^2
where k is the Coulomb constant, r is the distance between the charges, and q1 and q2 are the magnitudes of the charges.
In our case, r is given by:
r = √(x^2 + y^2)
The x-component of the force F1 is given by:
Fx1 = F1 cosθ
where θ is the angle between the force vector and the x-axis.
To find θ, we draw a line from q1 to q2 and extend it to meet the x-axis at point P as shown in the figure below:
From the figure, we can see that:
tanθ = y / x
Therefore,
cosθ = x / r
Substituting the value of r and cosθ in the expression for Fx1, we get:
Fx1 = kq1q2x / (x^2 + y^2)^(3/2)
To find the value of x that maximizes Fx1, we differentiate Fx1 with respect to x and equate it to zero:
dFx1/dx = kq1q2[(x^2 + y^2)^(3/2) - 3x^2(x^2 + y^2)^(1/2)] / (x^2 + y^2)^3 = 0
Solving for x, we get:
x = y / √2
Therefore, the value of x for the x-component of the force on q1 to be maximum is x = y / √2.
Answer: x = y / √2.
Solution:
To find the value of x for the x-component of the force on q1 to be maximum, we need to find the expression for the force acting on q1, and then differentiate it with respect to x to find the value of x that maximizes the force.
Let us consider the charges -q1 and -q2 at their respective positions as shown in the figure below:
From Coulomb's law, the force F1 on charge q1 due to charge q2 is given by:
F1 = kq1q2 / r^2
where k is the Coulomb constant, r is the distance between the charges, and q1 and q2 are the magnitudes of the charges.
In our case, r is given by:
r = √(x^2 + y^2)
The x-component of the force F1 is given by:
Fx1 = F1 cosθ
where θ is the angle between the force vector and the x-axis.
To find θ, we draw a line from q1 to q2 and extend it to meet the x-axis at point P as shown in the figure below:
From the figure, we can see that:
tanθ = y / x
Therefore,
cosθ = x / r
Substituting the value of r and cosθ in the expression for Fx1, we get:
Fx1 = kq1q2x / (x^2 + y^2)^(3/2)
To find the value of x that maximizes Fx1, we differentiate Fx1 with respect to x and equate it to zero:
dFx1/dx = kq1q2[(x^2 + y^2)^(3/2) - 3x^2(x^2 + y^2)^(1/2)] / (x^2 + y^2)^3 = 0
Solving for x, we get:
x = y / √2
Therefore, the value of x for the x-component of the force on q1 to be maximum is x = y / √2.
Answer: x = y / √2.
Community Answer
A charge -q1 is kept at a distance y from the origin on Y-axis and ano...
1
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
A charge -q1 is kept at a distance y from the origin on Y-axis and another charge -q2 is kept at a distance x from the origin on X-axis. The value of x for the x-component of the force on q1 to be maximum is1) x = y/22) x =y/√23) x= y4) x= √2y
Question Description
A charge -q1 is kept at a distance y from the origin on Y-axis and another charge -q2 is kept at a distance x from the origin on X-axis. The value of x for the x-component of the force on q1 to be maximum is1) x = y/22) x =y/√23) x= y4) x= √2y for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A charge -q1 is kept at a distance y from the origin on Y-axis and another charge -q2 is kept at a distance x from the origin on X-axis. The value of x for the x-component of the force on q1 to be maximum is1) x = y/22) x =y/√23) x= y4) x= √2y covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A charge -q1 is kept at a distance y from the origin on Y-axis and another charge -q2 is kept at a distance x from the origin on X-axis. The value of x for the x-component of the force on q1 to be maximum is1) x = y/22) x =y/√23) x= y4) x= √2y.
A charge -q1 is kept at a distance y from the origin on Y-axis and another charge -q2 is kept at a distance x from the origin on X-axis. The value of x for the x-component of the force on q1 to be maximum is1) x = y/22) x =y/√23) x= y4) x= √2y for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A charge -q1 is kept at a distance y from the origin on Y-axis and another charge -q2 is kept at a distance x from the origin on X-axis. The value of x for the x-component of the force on q1 to be maximum is1) x = y/22) x =y/√23) x= y4) x= √2y covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A charge -q1 is kept at a distance y from the origin on Y-axis and another charge -q2 is kept at a distance x from the origin on X-axis. The value of x for the x-component of the force on q1 to be maximum is1) x = y/22) x =y/√23) x= y4) x= √2y.
Solutions for A charge -q1 is kept at a distance y from the origin on Y-axis and another charge -q2 is kept at a distance x from the origin on X-axis. The value of x for the x-component of the force on q1 to be maximum is1) x = y/22) x =y/√23) x= y4) x= √2y in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of A charge -q1 is kept at a distance y from the origin on Y-axis and another charge -q2 is kept at a distance x from the origin on X-axis. The value of x for the x-component of the force on q1 to be maximum is1) x = y/22) x =y/√23) x= y4) x= √2y defined & explained in the simplest way possible. Besides giving the explanation of
A charge -q1 is kept at a distance y from the origin on Y-axis and another charge -q2 is kept at a distance x from the origin on X-axis. The value of x for the x-component of the force on q1 to be maximum is1) x = y/22) x =y/√23) x= y4) x= √2y, a detailed solution for A charge -q1 is kept at a distance y from the origin on Y-axis and another charge -q2 is kept at a distance x from the origin on X-axis. The value of x for the x-component of the force on q1 to be maximum is1) x = y/22) x =y/√23) x= y4) x= √2y has been provided alongside types of A charge -q1 is kept at a distance y from the origin on Y-axis and another charge -q2 is kept at a distance x from the origin on X-axis. The value of x for the x-component of the force on q1 to be maximum is1) x = y/22) x =y/√23) x= y4) x= √2y theory, EduRev gives you an
ample number of questions to practice A charge -q1 is kept at a distance y from the origin on Y-axis and another charge -q2 is kept at a distance x from the origin on X-axis. The value of x for the x-component of the force on q1 to be maximum is1) x = y/22) x =y/√23) x= y4) x= √2y tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup