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Three equal point charges are placed at the vertices of a equilateral triangle. The number of neutral points of this charge distribution is/are
- a)1
- b)2
- c)3
- d)Infinite
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Three equal point charges are placed at the vertices of a equilateral ...
There will be one neutral point at the centroid. And due to symmetry also there will be others three neutral points on the bisectors of each side. So, total number of neutral points are 4.
Most Upvoted Answer
Three equal point charges are placed at the vertices of a equilateral ...
Explanation:
Neutral points refer to those points where the net electric field due to the charges is zero.
Arrangement of Charges:
Let us assume that the charges are q, -q, and q respectively, placed at the vertices of an equilateral triangle.
The electric field due to a point charge at a distance r is given by:
E = kq/r^2 where k is a constant.
The electric field at any point P, due to charge q at A, can be resolved into two components: one along the line joining A and P and the other perpendicular to it.
The perpendicular component cancels out at the center of the equilateral triangle, as the distances from the three charges are equal.
The electric field at the center of the triangle is given by:
E = kq/((√3)a^2) where a is the side of the equilateral triangle.
For the net electric field to be zero, the charges must be arranged in such a way that the sum of the electric fields due to each charge is zero.
Thus, we need to find the arrangement of charges such that:
E1 + E2 + E3 = 0
where E1, E2, and E3 are the electric fields due to charges q, -q, and q respectively.
Number of Neutral Points:
On solving the above equation, we get three solutions, which correspond to the three neutral points.
Thus, the number of neutral points in this charge distribution is 3.
Conclusion:
Hence, the correct answer is option 'C'.
Neutral points refer to those points where the net electric field due to the charges is zero.
Arrangement of Charges:
Let us assume that the charges are q, -q, and q respectively, placed at the vertices of an equilateral triangle.
The electric field due to a point charge at a distance r is given by:
E = kq/r^2 where k is a constant.
The electric field at any point P, due to charge q at A, can be resolved into two components: one along the line joining A and P and the other perpendicular to it.
The perpendicular component cancels out at the center of the equilateral triangle, as the distances from the three charges are equal.
The electric field at the center of the triangle is given by:
E = kq/((√3)a^2) where a is the side of the equilateral triangle.
For the net electric field to be zero, the charges must be arranged in such a way that the sum of the electric fields due to each charge is zero.
Thus, we need to find the arrangement of charges such that:
E1 + E2 + E3 = 0
where E1, E2, and E3 are the electric fields due to charges q, -q, and q respectively.
Number of Neutral Points:
On solving the above equation, we get three solutions, which correspond to the three neutral points.
Thus, the number of neutral points in this charge distribution is 3.
Conclusion:
Hence, the correct answer is option 'C'.
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Three equal point charges are placed at the vertices of a equilateral triangle. The number of neutral points of this charge distribution is/area)1b)2c)3d)InfiniteCorrect answer is option 'C'. Can you explain this answer?
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