Electric field at a far away distance r on the axis of a dipole is E0. What is the electric field at a distance 2r on perpendicular bisector?AE016B−E016CE08D−E08

To find the electric field at a distance 2r on the perpendicular bisector of a dipole, we can use the principle of superposition.

Step 1: Consider the electric field due to the positive charge of the dipole at the point 2r on the perpendicular bisector. Let's call this electric field E1.

Step 2: The distance between the positive charge and the point 2r is r. Using the formula for the electric field due to a point charge, we can calculate E1 as E1 = k * q / r^2, where k is the electrostatic constant and q is the magnitude of the charge.

Step 3: Now, consider the electric field due to the negative charge of the dipole at the point 2r on the perpendicular bisector. Let's call this electric field E2.

Step 4: The distance between the negative charge and the point 2r is also r. Using the same formula as before, we can calculate E2 as E2 = k * q / r^2.

Step 5: Since the electric field is a vector quantity, we need to consider the direction as well. The electric field due to the positive charge points away from it, while the electric field due to the negative charge points towards it. Therefore, E1 and E2 have opposite directions.

Step 6: To find the net electric field at the point 2r on the perpendicular bisector, we need to add the electric fields E1 and E2. Since they have opposite directions, we subtract their magnitudes: E_net = E1 - E2.

Step 7: Substituting the values of E1 and E2, we get E_net = (k * q / r^2) - (k * q / r^2) = 0.

Therefore, the electric field at a distance 2r on the perpendicular bisector of a dipole is zero.