The square of resultant of two equal electric field vectors is three times their product. Angle between them is

Step-by-step solution

Let the two equal electric field vectors be E₁ and E₂ such that | E₁ | = | E₂ | = E . The resultant vector R = E₁ + E₂ has a magnitude given by R^2 = E^2 + E^2 + 2E^2 , where is the angle between the two vectors. R^2 = 2E^2(1 + ) = 2E^2(2 ^2 2 ) = 4E^2 ^2 2 . The problem states that the square of the resultant is three times the product of the magnitudes of the two vectors, which is 3(E E) = 3E^2 . Equating the two expressions for R^2 : 4E^2 ^2 2 = 3E^2 ^2 2 = 3 4 2 = 3 2 2 = 6 = 3 Answer: 3