Conducting wire of parabolic shape, initially `y=x^(2)` is moving with velocity `vec(V)=v_(0) hati` in a non-uniform magnetic field `vec(B)=B_(0)(1+(y/L)^(beta))hatk` as shown in figure. If `V_(0) , B_(0) L` and B are +ve constant `Deltaphi` is potential difference develop between the ends of wire, then correct statements (s) is/are

Options

A. `|Deltaphi|` remains the same if the parabolic wire is replaced by a straight wire, `y = x` initially, of length `sqrt(2)L`
B. `|Deltaphi|=(1)/(2)B_(0)V_(0)L" for "beta=0`

C. `|Deltaphi|` is proportional to the length of the wire projected on the y-axis.
D. `|Deltaphi|=(4)/(3)B_(0)V_(0)L" for "beta=2`

Answer

A, C, D