Physics, 14.04.2020 22:11 hiitslillyhere

Point PP is a distance d1d1 = 4.0 mm above a large sheet of metal that carries a current of 35 AA in the positive xx direction and a distance d2d2 = 3.0 mm below a very long wire that carries a current of 0.41 AA in the positive xx direction. If the magnetic field magnitude at P is zero, calculate the width of the metal sheet.

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Answer from: jaejaeJae9534

The width of the sheet is w =0.8046m

Explanation:

From the question we are told that

The distance of point P above a large sheet of metal is $D = 4.0mm =\frac{4}{1000} = 0.004m$

The current on the large metal sheet is I =34A

The distance of the the point P below a long wire $d = 3.0mm = \frac{3}{1000} = 0.003m$

The current on the long wire is I_w = 0.41A

The magnetic field at P is B = 0T

Generally magnetic field of P long wire is mathematically represented as

$B_w = \frac{\mu_o I_w}{2\pi r}$

Generally magnetic field of P large sheet of meta is mathematically represented as

$B_m = \frac{\mu_o K}{2}$

Where K is the current per unit width

The total magnetic field at P is

$\frac{\mu_o I_w}{2 \pi r} = \frac{\mu_o K}{2}$

Making K the subject of formula

$K = \frac{2 I_w }{2 \pi r }$

Substituting values

$K = \frac{2 * 0.41 }{2 * 3.142 * (0.0030) }$

K = 43.4967 A/m

Generally K is mathematically represented as

$K = \frac{I}{w}$

Where w is the width of the large sheet

Therefore the width of the metal sheet $w = \frac{I}{K}$

$= \frac{35}{43.4967}$

w =0.8046m

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