Four charges +5μC, +6μC ,-3μC and 2μC are located respectively at the corners A,B,C and D of a rectangle of sides 30cm and 40cm .Calculate the magnitude and direction of the net electric field at the center of the rectangle.
To calculate the magnitude and direction of the net electric field at the center of the rectangle, we can use the principle of superposition. The net electric field at a point due to multiple charges is the vector sum of the electric fields created by each individual charge.
Here are the steps to calculate the magnitude and direction of the net electric field at the center of the rectangle:
1. Calculate the electric fields created by each individual charge at the center of the rectangle.
- The electric field created by a point charge can be calculated using Coulomb's law:
Electric field (E) = (k * q) / r^2
Where k is the Coulomb's constant (9 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the charge to the point where the electric field is being calculated.
2. Determine the distance between each charge and the center of the rectangle.
- For the given rectangle with sides 30 cm and 40 cm, the center of the rectangle will be at the point where the diagonals intersect.
3. Calculate the electric field created by each charge at the center of the rectangle.
- Use the formula mentioned earlier for each charge, taking into account the distance between the charge and the center of the rectangle.
4. Determine the direction of each electric field.
- The direction of the electric field created by a positive charge is radially outward from the charge. The direction of the electric field created by a negative charge is radially inward toward the charge.
5. Add the electric fields vectorially to obtain the net electric field.
- Add the electric fields obtained in step 3, taking into account both magnitude and direction.
6. Calculate the magnitude and direction of the net electric field.
- Use the Pythagorean theorem to find the magnitude of the net electric field from the vector sum of the electric fields obtained in step 5.
- Use trigonometry to determine the direction of the net electric field. The direction will be the angle made by the resultant electric field with respect to a reference axis.
By following these steps, you will be able to calculate the magnitude and direction of the net electric field at the center of the rectangle.