A small coil of N turns has its plane perpendicular to a uniform magnetic field as shown in Fig. 30-5. The coil is connected to a Ballistic galvanometer, a device designed to measure the total charge passing through it. Find the charge passing through the coil if the coil is rotated through 180° about its diameter.

Explanation

As we stated just now, the total charge flown is the integral of the current:
`Q=intdQ=intIdt`
The current is related to the emf by Ohm.s law as
`I=E/R`
and the emf is only due to the changing magnetic flux, that is
`E=(dphi_(B))/(dt)`
Thus, the induced current is given by
`I=E/R=1/R(dphi_(B))/(dt)`

Substituting it back in Eq. 30-6, we get
`Q=intIdt=(Deltaphi_(B))/R`
The initial flux through the loop is given by
`phi_(i)=NBA`
and after rotating the loop through 180°, the flux would be
`phi_(f)=-NBA`
Hence, the charge flowing through the Ballistic galvanometer is given by
`Q=(2NBA)/R`
Note that the charge Q is independent of the time involved in rotating the coil-all that matters is the change in magnetic flux. A coil used in this way is called a flip coil. It is used to measure magnetic fields. For example, if the Ballistic galvanometer measures a total charge Q passing through the coil when it is flipped, the magnetic field can be found from the equation above.