An electric dipole is constructed by fixing two circular charged rings...
An electric dipole is constructed by fixing two circular charged rings of equal and opposite charge. The dipole moment is calculated about the point of contact assuming the z-axis passes through the rings.
Explanation:
To calculate the dipole moment, we need to determine the charge distribution and the distance between the charges. Let's break down the problem into smaller steps:
1. Charge Distribution:
Each circular charged ring contains a total charge Q, uniformly distributed. One ring has a positive charge and the other has an equal negative charge. The charges are fixed in place and do not move.
2. Dipole Moment:
The dipole moment is a measure of the separation between the positive and negative charges. It is defined as the product of the charge magnitude and the distance between them. In this case, since the charges are fixed on the circular rings, the dipole moment can be calculated as the product of the charge and the distance between the rings.
3. Distance Calculation:
To calculate the distance between the charges, we need to consider the geometry of the problem. The two circular rings are fixed in place with an insulating contact. Assuming the z-axis passes through the rings, the distance between the charges can be determined as the sum of the radii of the two rings.
4. Dipole Moment Calculation:
The dipole moment (p) is given by the formula p = Q * d, where Q is the charge magnitude and d is the distance between the charges. In this case, since the charges are equal and opposite, the dipole moment can be written as p = Q * 2a, where a is the radius of each ring.
5. Conclusion:
The dipole moment of the electric dipole constructed by fixing two circular charged rings can be calculated as p = Q * 2a, where Q is the charge magnitude and a is the radius of each ring. The dipole moment represents the separation between the positive and negative charges and is a crucial parameter in understanding the behavior of electric dipoles in electric fields.