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In a regular polygon of n sides, each corner is at a distance r from the centre. Identical charges of magnitude Q are placed at ( n-1) corners. The field at the centre is:?
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In a regular polygon of n sides, each corner is at a distance r from t...
Electric field can be superimposed, that means it can be added as a sum any number of electric fields.
Consider the n sided polygon with charges at each and every corner. Let the electric field at center in this case be E. Now remove one of the charges. Let the field at center due to (n - 1) charges be E₁ and field due to the remaining one charge be E₂.
According to principle of superimposition,
E = E₁ + E₂
We know that E = 0 since in that case charges are placed symmetrically. So,
E₁ = - E₂ (field at center due to 1 charge)
E₁ = - Q/4πεr²
Note: The similar concept cannot be applied to electric potential because it is scalar and not a vector.
Consider the n sided polygon with charges at each and every corner. Let the electric field at center in this case be E. Now remove one of the charges. Let the field at center due to (n - 1) charges be E₁ and field due to the remaining one charge be E₂.
According to principle of superimposition,
E = E₁ + E₂
We know that E = 0 since in that case charges are placed symmetrically. So,
E₁ = - E₂ (field at center due to 1 charge)
E₁ = - Q/4πεr²
Note: The similar concept cannot be applied to electric potential because it is scalar and not a vector.
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In a regular polygon of n sides, each corner is at a distance r from t...
**Field at the Centre of a Regular Polygon**
To find the electric field at the center of a regular polygon, we can consider the electric field contribution from each charge at the corners of the polygon.
**Electric Field Contribution from each Charge**
The electric field contribution from each charge at the corners of the polygon can be calculated using Coulomb's Law. Coulomb's Law states that the magnitude of the electric field due to a point charge is given by:
E = k * Q / r^2
where E is the electric field, k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2), Q is the magnitude of the charge, and r is the distance between the charge and the point where the electric field is being measured.
**Electric Field from each Corner**
In a regular polygon of n sides, each corner is at a distance r from the center. Identical charges of magnitude Q are placed at (n-1) corners. Therefore, the electric field contribution from each charge at the corners can be given as:
E = k * Q / r^2
Since there are (n-1) charges at the corners, the total electric field at the center can be calculated by considering the vector sum of the electric field contributions from each charge.
**Vector Sum of Electric Fields**
Since the charges are placed at the corners of the polygon, their positions can be represented as vectors. Let's denote the position vector of each charge as r_i, where i ranges from 1 to (n-1).
To calculate the total electric field at the center, we need to calculate the vector sum of the electric field contributions from each charge. This can be done by summing up the individual electric field vectors.
E_total = E_1 + E_2 + ... + E_(n-1)
**Magnitude of Total Electric Field**
The magnitude of the total electric field at the center can be calculated by taking the magnitude of the vector sum.
|E_total| = |E_1 + E_2 + ... + E_(n-1)|
Since the charges are placed symmetrically at the corners of the regular polygon, the electric field contributions from each charge will cancel out in pairs. This is because the electric field vectors from opposite charges will have equal magnitudes but opposite directions.
Therefore, the magnitude of the total electric field at the center of the regular polygon will be zero.
To find the electric field at the center of a regular polygon, we can consider the electric field contribution from each charge at the corners of the polygon.
**Electric Field Contribution from each Charge**
The electric field contribution from each charge at the corners of the polygon can be calculated using Coulomb's Law. Coulomb's Law states that the magnitude of the electric field due to a point charge is given by:
E = k * Q / r^2
where E is the electric field, k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2), Q is the magnitude of the charge, and r is the distance between the charge and the point where the electric field is being measured.
**Electric Field from each Corner**
In a regular polygon of n sides, each corner is at a distance r from the center. Identical charges of magnitude Q are placed at (n-1) corners. Therefore, the electric field contribution from each charge at the corners can be given as:
E = k * Q / r^2
Since there are (n-1) charges at the corners, the total electric field at the center can be calculated by considering the vector sum of the electric field contributions from each charge.
**Vector Sum of Electric Fields**
Since the charges are placed at the corners of the polygon, their positions can be represented as vectors. Let's denote the position vector of each charge as r_i, where i ranges from 1 to (n-1).
To calculate the total electric field at the center, we need to calculate the vector sum of the electric field contributions from each charge. This can be done by summing up the individual electric field vectors.
E_total = E_1 + E_2 + ... + E_(n-1)
**Magnitude of Total Electric Field**
The magnitude of the total electric field at the center can be calculated by taking the magnitude of the vector sum.
|E_total| = |E_1 + E_2 + ... + E_(n-1)|
Since the charges are placed symmetrically at the corners of the regular polygon, the electric field contributions from each charge will cancel out in pairs. This is because the electric field vectors from opposite charges will have equal magnitudes but opposite directions.
Therefore, the magnitude of the total electric field at the center of the regular polygon will be zero.
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In a regular polygon of n sides, each corner is at a distance r from the centre. Identical charges of magnitude Q are placed at ( n-1) corners. The field at the centre is:?
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In a regular polygon of n sides, each corner is at a distance r from the centre. Identical charges of magnitude Q are placed at ( n-1) corners. The field at the centre is:? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about In a regular polygon of n sides, each corner is at a distance r from the centre. Identical charges of magnitude Q are placed at ( n-1) corners. The field at the centre is:? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a regular polygon of n sides, each corner is at a distance r from the centre. Identical charges of magnitude Q are placed at ( n-1) corners. The field at the centre is:?.
In a regular polygon of n sides, each corner is at a distance r from the centre. Identical charges of magnitude Q are placed at ( n-1) corners. The field at the centre is:? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about In a regular polygon of n sides, each corner is at a distance r from the centre. Identical charges of magnitude Q are placed at ( n-1) corners. The field at the centre is:? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a regular polygon of n sides, each corner is at a distance r from the centre. Identical charges of magnitude Q are placed at ( n-1) corners. The field at the centre is:?.
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