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Magnetic Field

Consider two ...

Question

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. $V_{1}$ 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 statement(s) is (are)

A

If

w_{1} = w_{2}

and

d_{1} = 2 d_{2}

, then

V_{2} = 2 V_{1}

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B

If

w_{1} = w_{2}

and

d_{1} = 2 d_{2}

, then

V_{2} = V_{1}

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C

If

w_{1} = 2 w_{2}

and

d_{1} = d_{2}

, then

V_{2} = 2 V_{1}

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D

If

w_{1} = 2 w_{2}

and

d_{1} = d_{2}

, then

V_{2} = V_{1}

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Solution

The correct options are
A If $w_{1} = w_{2}$ and $d_{1} = 2 d_{2}$ , then $V_{2} = 2 V_{1}$
D If $w_{1} = 2 w_{2}$ and $d_{1} = d_{2}$ , then $V_{2} = V_{1}$
$q v B = \frac{q (V_{m} - V_{k})}{w}$
$V_{m} - V_{k} = w v B$
$I = n e A v = n e (w d) v$
$w v = \frac{I}{n e d}$
$V_{m} - V_{k} = \frac{I}{n e d} B$
For the case of option A
$w_{1} = w_{2}, d_{1} = 2 d_{2}$ Thus $V_{2} = 2 V_{1}$
For the case of option D

$w_{1} = 2 w_{2}, d_{1} = d_{2}$ Thus $V_{2} = V_{1}$

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