A condenser has two conducting plates of radius  $10cm$ separated by a distance of  $5mm$. It is charged with a constant current of  $0.15A$. The magnetic field at a point $2cm$ from the axis in the gap is

detailed solution

Correct option is C

Consider a loop of radius 'r' between the two circular plates, placed axially with them. The area of the loop, A'=πr2 By symmetry magnetic field induction B→ is equal in magnitude and is tangential to the circle at every point In this case, only displacement current  ID, will cross the loop. Therefore, using Ampere’s Maxwell law, we have ∮B→.dl→=μ0ID⇒2πrB=μ0×(current passing through the area A') ⇒ 2πrB=μ0Iπr2πR2 ⇒B=μ0ID2πr×rR2    ⇒ B=μ0I2π×rR2 ⇒B=2×10−7×0.15×2×10−210−2                     ⇒ B=6×10−8T