The magnitude of the electric field at a distance d on the equatorial line of a short electric dipole is E₀ . At a distance x on the axial line of the same dipole, the magnitude of the electric field is 128 E₀ . If x = d N , the value of N is

Step-by-step solution

For a short electric dipole, the magnitude of the electric field on the equatorial line at a distance d is given by: E₀ = kp d^3 The magnitude of the electric field on the axial line at a distance x is: E_ ax = 2kp x^3 Given that E_ ax = 128 E₀ , we can substitute the expressions: 2kp x^3 = 128 ( kp d^3 ) Dividing both sides by 2kp : 1 x^3 = 64 d^3 Taking the cube root of both sides: 1 x = 4 d x = d 4 Comparing this with x = d N , we get N = 4 . Answer: 4