Magnetics 6 Question 19
19. Consider two different metallic strips ( 1 and 2$)$ of the same material. Their lengths are the same, widths are $w _1$ and $w _2$ and thicknesses are $d _1$ and $d _2$, respectively. Two points $K$ and $M$ are symmetrically located on the opposite faces parallel to the $x-y$ plane (see figure). $V _1$ and $V _2$ are the potential differences between $K$ and $M$ in strips 1 and 2, respectively. Then, for a given current $I$ flowing through them in a given magnetic field strength $B$, the correct statements is/are
(2015 Adv.)
(a) If $w _1=w _2$ and $d _1=2 d _2$, then $V _2=2 V _1$
(b) If $w _1=w _2$ and $d _1=2 d _2$, then $V _2=V _1$
(c) If $w _1=2 w _2$ and $d _1=d _2$, then $V _2=2 V _1$
(d) If $w _1=2 w _2$ and $d _1=d _2$, then $V _2=V _1$
Show Answer
Solution:
- $F _B=B e v=B e \frac{I}{n A e}=\frac{B I}{n A}$
$$ F _e=e E $$
$$ \begin{aligned} F _e & =F _B \\ e E & =\frac{B I}{n A} \Rightarrow E=\frac{B}{n A e} \\ V & =E d=\frac{B I}{n A e} \cdot w=\frac{B I w}{n(w d) e}=\frac{B I}{n e d} \\ \frac{V _1}{V _2} & =\frac{d _2}{d _1} \\ \Rightarrow \text { if } \quad w _1 & =2 w _2 \end{aligned} $$
and $d _1=d _2$
$$ V _1=V _2 $$
