Two charges of - 4 μC and + 4 μC are placed at the points A ( 1 , 0 , 4 ) m and B ( 2 , - 1 , 5 ) m located in an electric field E → = 0 . 20 i ^ V cm - 1 . The magnitude of the torque acting on the dipole is 8 α × 10 - 5 N m , where α = _________.

Step-by-step solution

Given the electric field is E → = 0 . 20 i ^ V cm = 20 i ^ V m The formula for calculating the torque is τ → = p → × E → . . . 1 where, p → = q l → = 4 × 2 i ^ + - 1 j ^ + 5 k ^ - 1 i ^ + 0 j ^ + 4 k ^ = 4 i ^ - j ^ + k ^ μC m Thus, from equation (1), it follows that τ → = ( 4 i ^ - 4 j ^ + 4 k ^ ) × 10 - 6 × ( 20 i ^ ) N m = ( 8 k ^ + 8 j ^ ) × 10 - 5 N m ⇒ τ → = 8 2 + 8 2 × 10 - 5 N m = 8 2 × 10 - 5 N m Hence, α = 2 .