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Four particles each having a charge q, are placed on the four vertices of a regular pentagon. The distance of each corner from the centre is a. Find the electric field at the centre of the pentagon?
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Four particles each having a charge q, are placed on the four vertices...
Charges are present on corners B, C, D, E.
Total electric force will be along the direction OA.
Magnitude of force = 2 x (1/ 4πε) x (q/a^2) x cos 36 degrees - 2 x (1/ 4πε) x (q/a^2) x cos 72 degrees
= (1/ 4πε) x (q/a^2)
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Four particles each having a charge q, are placed on the four vertices...
Problem: Four particles each having a charge q are placed on the four vertices of a regular pentagon. The distance of each corner from the centre is a. Find the electric field at the centre of the pentagon.
Solution:
To find the electric field at the centre of the pentagon, we can use the principle of superposition. We can find the electric field at the centre due to each charge and then add them up to get the total electric field.
Electric field due to one charge:
The electric field due to a point charge q at a distance r is given by Coulomb's law:
E = kq/r^2
where k is the Coulomb constant (k = 9 x 10^9 Nm^2/C^2).
In this case, the distance between each charge and the centre of the pentagon is a, so the electric field due to one charge at the centre is:
E = kq/a^2
Electric field due to all charges:
To find the electric field due to all charges, we add up the electric fields due to each charge. Since the charges are at the vertices of a regular pentagon, we can divide them into two sets of two charges each, and find the electric field due to each set.
Electric field due to one set of charges:
Consider the two charges that are opposite to each other. The distance between them is 2a, and the electric field due to this set of charges at the centre is:
E1 = kq/(2a)^2 = kq/4a^2
Electric field due to the other set of charges:
Consider the other two charges that are adjacent to each other. The distance between them is a, and the electric field due to this set of charges at the centre is:
E2 = kq/a^2
Total electric field:
The total electric field at the centre is the vector sum of the electric fields due to each set of charges. Since the two sets are at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the total electric field:
E = sqrt(E1^2 + E2^2) = sqrt((kq/4a^2)^2 + (kq/a^2)^2) = kq/a^2 * sqrt(5)/2
Therefore, the electric field at the centre of the pentagon is:
E = kq/a^2 * sqrt(5)/2
Conclusion:
The electric field at the centre of the pentagon due to the four charges placed at the vertices is kq/a^2 * sqrt(5)/2.
Solution:
To find the electric field at the centre of the pentagon, we can use the principle of superposition. We can find the electric field at the centre due to each charge and then add them up to get the total electric field.
Electric field due to one charge:
The electric field due to a point charge q at a distance r is given by Coulomb's law:
E = kq/r^2
where k is the Coulomb constant (k = 9 x 10^9 Nm^2/C^2).
In this case, the distance between each charge and the centre of the pentagon is a, so the electric field due to one charge at the centre is:
E = kq/a^2
Electric field due to all charges:
To find the electric field due to all charges, we add up the electric fields due to each charge. Since the charges are at the vertices of a regular pentagon, we can divide them into two sets of two charges each, and find the electric field due to each set.
Electric field due to one set of charges:
Consider the two charges that are opposite to each other. The distance between them is 2a, and the electric field due to this set of charges at the centre is:
E1 = kq/(2a)^2 = kq/4a^2
Electric field due to the other set of charges:
Consider the other two charges that are adjacent to each other. The distance between them is a, and the electric field due to this set of charges at the centre is:
E2 = kq/a^2
Total electric field:
The total electric field at the centre is the vector sum of the electric fields due to each set of charges. Since the two sets are at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the total electric field:
E = sqrt(E1^2 + E2^2) = sqrt((kq/4a^2)^2 + (kq/a^2)^2) = kq/a^2 * sqrt(5)/2
Therefore, the electric field at the centre of the pentagon is:
E = kq/a^2 * sqrt(5)/2
Conclusion:
The electric field at the centre of the pentagon due to the four charges placed at the vertices is kq/a^2 * sqrt(5)/2.
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Four particles each having a charge q, are placed on the four vertices of a regular pentagon. The distance of each corner from the centre is a. Find the electric field at the centre of the pentagon?
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Four particles each having a charge q, are placed on the four vertices of a regular pentagon. The distance of each corner from the centre is a. Find the electric field at the centre of the pentagon? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Four particles each having a charge q, are placed on the four vertices of a regular pentagon. The distance of each corner from the centre is a. Find the electric field at the centre of the pentagon? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four particles each having a charge q, are placed on the four vertices of a regular pentagon. The distance of each corner from the centre is a. Find the electric field at the centre of the pentagon?.
Four particles each having a charge q, are placed on the four vertices of a regular pentagon. The distance of each corner from the centre is a. Find the electric field at the centre of the pentagon? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Four particles each having a charge q, are placed on the four vertices of a regular pentagon. The distance of each corner from the centre is a. Find the electric field at the centre of the pentagon? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four particles each having a charge q, are placed on the four vertices of a regular pentagon. The distance of each corner from the centre is a. Find the electric field at the centre of the pentagon?.
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