Potential difference across the strips of an inductor The voltage across the ends of an inductor is  $L (di/dt)$. Applying the loop law  $V = L(di/dt)$, so the voltage across the strips at a distance x measured from the "LEFT END" should be $V \frac xl$ because the inductance of x length is $ L \frac xl$.
But according to the answer given it should be $ V( 1 - \frac xl)$. Why?
What do we mean when we say voltage across strips? Any help is highly appreciated.

 A: There are 2 different potential differences in this question. One is the PD along each strip in the direction of $l$ - ie horizontal. I shall call this $V_x$. The other is the PD between the 2 strips in the direction of $b$ - ie vertical - at the same horizontal position $x$. I shall call this $V_y$, but note that like $V_x$ it also depends on $x$.
Option D is asking for an expression for $V_y$.
If the current has reached a limiting constant value, which will happen after the battery has been connected for a long time, then the PD $V_x$ along each strip depends only on its resistance not its inductance, because there is no back emf in an inductor if the current through it is not changing. In this case the vertical PD between the strips increases linearly from $0$ to $V_0$ when measured from the RH end where they are shorted : $$V_y=V_0 \frac{x}{l}$$ 
Before the current becomes constant there is a potential drop $V_R=IR$ across each strip due to its resistance $R$. Initially $I$ is very small so $V_R=IR \ll \frac12 V_0$. At the same time there is a back emf of $V_L=L\frac{dI}{dt}$ while the current increases, where $L$ is inductance. This is also a potential drop across the inductor, and it is linear (proportional to $x$) because inductance $L$ like resistance $R$ is proportional to length. Initially $\frac{dI}{dt}$ is large and $V_L =L\frac{dI}{dt} \approx \frac12 V_0$.
The sum of these 2 PDs equals the PD supplied by the battery, the same as when there is a separate resistor and inductor in series : $$V_R+V_L=\frac12 V_0$$ So the total PD $V_x$ along each strip varies linearly even when the current is changing, and the PD $V_y$ between the 2 strips again increases linearly from the RH end, as in the above equation.    
