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A charge +4q is located on the X-axis of a Cartesian coordinate system at x = -2a as shown. Another charge +(q/4) is located on the X-axis at x = a. Where on the Y-axis should a third charge -3q be placed so that the resultant electric field at the origin O has equal positive X and Y components?
- a)y = 2a
- b)y = -3a
- c)y = -2a
- d)y = (3/4)a
Correct answer is option 'A'. Can you explain this answer?
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A charge +4q is located on the X-axis of a Cartesian coordinate system...
Solution:
Given,
Charge 1 (q1) = 4q at x = -2a
Charge 2 (q2) = q/4 at x = a
Charge 3 (q3) = -3q at some point on the Y-axis (y)
To find: y-coordinate of charge 3 (q3) such that the electric field at the origin has equal positive X and Y components.
Electric field at the origin due to charge 1 (q1):
E1 = (1/4πε0) * (4q) / (4a)^2
Electric field at the origin due to charge 2 (q2):
E2 = (1/4πε0) * (q/4) / a^2
Electric field at the origin due to charge 3 (q3):
E3 = (1/4πε0) * (-3q) / y^2
The electric field at the origin (E) can be obtained by vector addition of E1, E2, and E3. Since we need the electric field to have equal positive X and Y components, we can write:
E * cos(45°) = E * sin(45°)
Simplifying this equation, we get:
E1 + E2 - E3 = E1/√2
Substituting the values of E1, E2, and E3, we get:
(1/4πε0) * [4q/(4a)^2 + q/(4a^2) + 3q/y^2] = (1/4πε0) * 4q/(4a^2*√2)
Cancelling out common terms and simplifying, we get:
y = 2a
Therefore, the third charge should be placed at a distance of 2a from the origin along the Y-axis.
Given,
Charge 1 (q1) = 4q at x = -2a
Charge 2 (q2) = q/4 at x = a
Charge 3 (q3) = -3q at some point on the Y-axis (y)
To find: y-coordinate of charge 3 (q3) such that the electric field at the origin has equal positive X and Y components.
Electric field at the origin due to charge 1 (q1):
E1 = (1/4πε0) * (4q) / (4a)^2
Electric field at the origin due to charge 2 (q2):
E2 = (1/4πε0) * (q/4) / a^2
Electric field at the origin due to charge 3 (q3):
E3 = (1/4πε0) * (-3q) / y^2
The electric field at the origin (E) can be obtained by vector addition of E1, E2, and E3. Since we need the electric field to have equal positive X and Y components, we can write:
E * cos(45°) = E * sin(45°)
Simplifying this equation, we get:
E1 + E2 - E3 = E1/√2
Substituting the values of E1, E2, and E3, we get:
(1/4πε0) * [4q/(4a)^2 + q/(4a^2) + 3q/y^2] = (1/4πε0) * 4q/(4a^2*√2)
Cancelling out common terms and simplifying, we get:
y = 2a
Therefore, the third charge should be placed at a distance of 2a from the origin along the Y-axis.
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A charge +4q is located on the X-axis of a Cartesian coordinate system at x = -2a as shown. Another charge +(q/4) is located on the X-axis at x = a. Where on the Y-axis should a third charge -3q be placed so that the resultant electric field at the origin O has equal positive X and Y components?a)y = 2ab)y = -3ac)y = -2ad)y = (3/4)aCorrect answer is option 'A'. Can you explain this answer?
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A charge +4q is located on the X-axis of a Cartesian coordinate system at x = -2a as shown. Another charge +(q/4) is located on the X-axis at x = a. Where on the Y-axis should a third charge -3q be placed so that the resultant electric field at the origin O has equal positive X and Y components?a)y = 2ab)y = -3ac)y = -2ad)y = (3/4)aCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A charge +4q is located on the X-axis of a Cartesian coordinate system at x = -2a as shown. Another charge +(q/4) is located on the X-axis at x = a. Where on the Y-axis should a third charge -3q be placed so that the resultant electric field at the origin O has equal positive X and Y components?a)y = 2ab)y = -3ac)y = -2ad)y = (3/4)aCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A charge +4q is located on the X-axis of a Cartesian coordinate system at x = -2a as shown. Another charge +(q/4) is located on the X-axis at x = a. Where on the Y-axis should a third charge -3q be placed so that the resultant electric field at the origin O has equal positive X and Y components?a)y = 2ab)y = -3ac)y = -2ad)y = (3/4)aCorrect answer is option 'A'. Can you explain this answer?.
A charge +4q is located on the X-axis of a Cartesian coordinate system at x = -2a as shown. Another charge +(q/4) is located on the X-axis at x = a. Where on the Y-axis should a third charge -3q be placed so that the resultant electric field at the origin O has equal positive X and Y components?a)y = 2ab)y = -3ac)y = -2ad)y = (3/4)aCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A charge +4q is located on the X-axis of a Cartesian coordinate system at x = -2a as shown. Another charge +(q/4) is located on the X-axis at x = a. Where on the Y-axis should a third charge -3q be placed so that the resultant electric field at the origin O has equal positive X and Y components?a)y = 2ab)y = -3ac)y = -2ad)y = (3/4)aCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A charge +4q is located on the X-axis of a Cartesian coordinate system at x = -2a as shown. Another charge +(q/4) is located on the X-axis at x = a. Where on the Y-axis should a third charge -3q be placed so that the resultant electric field at the origin O has equal positive X and Y components?a)y = 2ab)y = -3ac)y = -2ad)y = (3/4)aCorrect answer is option 'A'. Can you explain this answer?.
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