A uniform electric field of 500 Vm ⁻¹ is directed at 30^ with the positive X -axis as shown in figure. The potential difference (V_B-V_A ) if O A=3 ~m and O B=5 ~m is

Step-by-step solution

Given, Electric field E₀=500 Vm ⁻¹ aligned E & = (E₀ i +E₀ j ) Vm ⁻¹ O A & =3 ~cm and O B=5 ~m aligned Now, displacement vector, A B =d r =(3 i +5 j ) m We know that, potential difference, V=- E d r i.e. V_B-V_A= (E₀ i +E₀ j ) (3 i +5 j ) Substituting the values, we get V_B-V_A=-500 ( 30^ i + 30^ j ) (3 i +5 j ) aligned & =-500 (3 30^ +5 30^ ) & =-500 [ 3 3 2 + 5 2 ] V aligned V_B-V_A=-250(3 3 +5) V