Two coils ' P ' and ' Q ' are separated by some distance. When a current of 3 A flows through coil ' P ' , a magnetic flux of 10 - 3 W b passes through ' Q ' . No current is passed through ' Q ' . When no current passes through ' P ' and a current of 2 A passes through ' Q ' , the flux through ' P ' is:

Step-by-step solution

Since the coils are co-axial, the flux through the coils can be written as the product of their surface area and the magnetic field produced by the coil along its axis. Consider the flux passing through Q ϕ Q = μ 0 i 1 R 2 2 R 2 + x 2 3 2 × π R 2 = 10 - 3   Wb And the flux passing through P: ϕ P = μ 0 i 1 r 2 2 R 2 + x 2 3 2 × π R 2 Taking the ratio ϕ P ϕ Q = i 2 i 1 × R 2 + x 2 3 2 R 2 + x 2 3 2 ⇒ ϕ P 10 - 3 = i 2 i 1 ⇒ ϕ P 10 - 3 =