Question

Consider three quantities $x=E/B,y=\sqrt{1/{\mu }_0{\epsilon }_0}$ and $Z=\frac{l}{CR}$. Here, $l$ is the length of a wire, $C$ is a capacitance and $R$ is a resistance. All other symbols have standard meanings.

• A. $x,y$ have the same dimensions
• B. $y,z$ have the same dimensions
• C. $z,x$ have the same dimensions
• D. the field at one point is opposite to that at the other point.

Answer 1

Answer: (A), (B), (C)

The correct options are
A $x,y$ have the same dimensions
B $y,z$ have the same dimensions
C $z,x$ have the same dimensions

As $E=Bv$, thus $X$ has a dimension of velocity.
Also, $c=\sqrt{\frac{1}{{\mu }_o{ϵ}_o}}$, where $c$ is the speed of light.
So $Y$ must have a dimension of velocity.
Now $Z=\frac{l}{CR}=l\times \frac{V}{Q}\times \frac{I}{V}=l\times \frac{1}{Q}\times \frac{Q}{t}=\frac{l}{t}$
Thus, $Z$ also has dimension of velocity.