A `10 Omega` coil of 180 turns and diameter 4 cm is placed in a uniform magnetic field so that the magnetic flux is maximum through the coil's cross-sectional area. When the field is suddenly removed a charge of 360 `muC` flows through a `618 Omega` galvanometer connected to the coil, find the magnetic field.

Options

A. 12 T
B. 6 T
C. 1 T
D. 8 T

Answer

C

Explanation

Given, resistance of a coil, `R=10 Omega`
number of turns in the coil, `N=180`
and diameter of the coil `=4` cm `=4xx10^(-2)` m
Magnetic flux associated with the coil is maximum.
Hence, `theta=0^(@)`
`:.` Magnetic flux, `phi=BA`
When magnetic field is suddenly removed, then some charge flows through the galvanometer. Given, resistance of a galvanometer, `R_(g)=618 Omega` and charge flowing through the galvanometer, `q=360 mu C=360xx10^(-6) C`
As `q=I.Delta t`
`implies q=e/R_(eq) Delta t=(Delta phi)/(Delta t).(Delta t)/R_(eq)" "( :' e=N (Delta phi)/(Delta t))`
So, for N turms, `q=N/R_(eq) Delta phi`
Here, `R_(eq)=R+R_(g)`
Putting the given values, we get
`360xx10^(-6)=180/((618+10)). (BA-0)`
`2xx10^(-6)xx628=B.pixx(2xx10^(-2))^(2)" "[ :' A=pi r^(2)]`
`implies B=(2xx10^(-6)xx628)/(3.14xx4xx10^(-4))=1 T`
Hence, the magnetic field is 1 T.