Consider a coil (of area A, resistance R and number of turns N) held perpendicular to a uniform magnetic field of strength B. The coil is now turned through `180^(@)` in the time `Delta t.` Total charge that flows through a given cross-section of the coil is .......

Options

A. `(NBA)/(R)`
B. `(2 NBA)/(R)`
C. `(NBA)/(2R)`
D. `(2 N BA)/(3R)`

Answer

B

Explanation

When plane of coil is prependicular to the magnetic field `theta = 0^(@)` and after it is rotated
through `180^(@) `
`implies` Initial flux ` = NB A cos 0^(@) = NBA`
and Final flux
`= NBA cos 180^(@) =- NBA`
`implies` Change in flux
`= | Delta phi | = NBA - ( - NBA)= 2 NBA`
`epsi = `Average induced
`emf = (| Delta phi | )/( Delta t ) = ( 2 N BA )/(Delta t )`
Average current `= (epsi )/(R) = (2 NBA)/(R Delta t)`
Average current `(Delta Q)/(Deltat) = (2NBA)/(R Deltat)`
`implies DeltaQ = (2NBA)/(R)`