Magnetic Circuits

Q. Two infinite strips of width w m in X-direction as shown in figure, are carrying forward and return currents of $+I$ and $-I$ in the Z-direction. The strips are separated by a distance of x m. The inductance per unit length of the configuration is measured to be L H/m. If the distance of separation between the strips is now reduced to 1/2 m, the inductance per unit length of the configuration is

1. 2L H/m
2. L/4 H/m
3. L/2 H/m
4. 4L H/m

Q. A uniform and constant magnetic field $B=\hat{z}B$ exists in the $\hat{z}$ direction in vacuum. A particle of mass m with a small charge q is introduced into this region with an initial velocity $v=\hat{x}{v}_x+\hat{z}{v}_z$. Given that B, m, q, $v_{x}and{v}_z$ are all non-zero. Which one of the following describes the eventual trajectory of the particle?

1. Helical motion in the $\hat{z}$ direction.
2. Circular motion in the xy plane
3. Linear motion in the $\hat{z}$ direction
4. Linear motion in the $\hat{x}$ direction.