What Are the Electric Field Components at the Center of a Charged Square?

[mousesgr]

Electricity and Magnetism urgent!help!

11. Electric charge is distributed uniformly along each side of a square. Each side of the square has length a. Two adjacent sides have positive charge with total charge +Q on each.
(i) If the other two sides have negative charge with total charge –Q on each, what are the x- and y-components of the resultant electric field at the center of the square?
(ii) Repeat the calculation of part (i) if all four sides have positive charge +Q.


12. A point charge is distance from the center of a dipole consisting of charges separated by distance . The charge is located in the plane that bisects the dipole. At this instant, what are (a) the force (magnitude and direction) and (b) the magnitude of the torque on the dipole? You can assume r >> s .

 

[mukundpa]

Where are you struck. We are helping to get you solving the problems, not solving the problems.

 

[quicknote]

11. The x-component of the resultant electric field at the center of the square can be calculated by considering the electric fields created by the two positive and two negative charges. Since the charges are uniformly distributed, the electric field at the center of the square due to the positive charges is given by E = kQ/a^2, where k is the Coulomb's constant. Similarly, the electric field at the center of the square due to the negative charges is also E = kQ/a^2. Since the electric fields created by the positive and negative charges are in opposite directions, the x-component of the resultant electric field is zero.

The y-component of the resultant electric field can be calculated by considering the electric fields created by the positive charges. Since the electric fields created by the positive charges are in the same direction, the y-component of the resultant electric field is given by Ey = 2E = 2kQ/a^2.

(ii) If all four sides of the square have positive charge +Q, then the electric field at the center of the square is given by E = 4kQ/a^2. Therefore, the x-component of the resultant electric field is zero and the y-component is given by Ey = 4kQ/a^2.

12. (a) The force on the dipole can be calculated using Coulomb's law, F = k(q1q2)/r^2, where k is the Coulomb's constant, q1 and q2 are the charges on the dipole, and r is the distance between the point charge and the center of the dipole. In this case, the force on the dipole is zero since the point charge is located in the plane that bisects the dipole and the forces created by the two charges on the dipole cancel out.

(b) The torque on the dipole can be calculated using the formula, τ = pEsinθ, where p is the dipole moment, E is the electric field, and θ is the angle between the dipole moment and the electric field. In this case, the torque is given by τ = 2psEsinθ, where s is the distance between the two charges on the dipole and E is the electric field at the center of the dipole due to the point charge. Since the electric field is perpendicular to the dipole moment, the angle θ is 90 degrees and sin