In the figure `B_(1)`, `B_(2)` and `B_(3)` represent uniform time varying magnetic fields in three different infinitely long cylindrical regions with axis passing through `P`, `Q` and `R` and perpendicular to the plane of the paper. `PQR` is an equilateral triangle of side `4sqrt(3)r`, where `r` is radius of each cylindrical region `(r=1m)`. The magnetic inductions vary with time `t` as `B_(1)=A+at`, `B_(2)=A-bt` and `B_(3)=A+ct`. Here `a=2 Tesla//s`, `b=2 Tesla//s` and `c=1 Tesla//s` and `A` is a constant with dimensions of magnetic field and `'t'` is time. Find the induced electric field strength at the centroid of the triangle `PQR`.

Explanation

The contribution due to any one the cylinder
`|E|=(r^(2))/(2x)|(dB)/(dt)|=(r^(2))/(8r)|(dB)/(dt)|=(1)/(8)|(dB)/(dt)|`
`|E_(1)|=(1)/(4)V//m`
`|E_(2)|=1//4V//m`
`|E_(3)|=1//8V//m`
(directions as shown in the figure)
`|vecE_(1)+vecE_(2)+vecE_(3)|=(sqrt(13))/(8)V//m`