Two solenoids

The magnetic field intensity depends upon the current flowing through the solenoid as well as the number of turns in the coil.

In $X$ , length is $20$ cm and current flowing is $1$ A while, in $Y$ , length is $40$ cm and current flowing is $2$ A. Moreover, the number of turns in both $X$ and $Y$ are same, i.e., constant here.

Now, if we consider the ratio of current flowing and length in $X$ and $Y$ , we find the ratio to be same, i.e., $\frac{2}{40}=\frac{1}{20}$ .

Thus, the electric field strength as well as the magnetic field intensity in both $X$ and $Y$ is the same, so the ratio is $\boxed{1:1}$

Hello,

as for solenoid X, as for magnetic field intensity B,let Bx for X, By for Y,

by applying B= unI ,as n = N/L, stated that Nx=Ny=N,

Bx = uN(1) / (20) = uN / 20,

By = uN(2) / (40) = uN /20,

By comparing Bx to By,

Bx / By = uN / 20 / uN /20

Bx / By = uN / 20 x 20 / uN

Bx / By = 1 / 1

Bx : By = 1:1

Thanks...