A current I is flowing in a straight conductor of length L. The magnetic induction at a point distant `(L)/(4)` from its centre will be

Explanation

The magnetic field induction B, length l and the velocity v of the conductor EF are mutually perpendicular, hence the emf induced in it is e=Blv (with end F of the rod at higher potential)
`:.` The effective electric circuit can be redrawn as shown in Fig.

The resistances `R_(1)` and `R_(2)` are in parallel, so the equivalent resistance R is given by `(1)/(R)=(1)/(R_(1))+(1)/(R_(2))`
From Ohms law, the total current is
`i=(e)/(R)" "i=Blv((1)/(R_(1))+(1)/(R_(2)))`
Current in AD is `i_(1)= (BI V)/(R_(1))`,
Current in BC is `i_(2) = (BlV)/(R_(2))`