91影视

The magnetic field created by the electric field equals the size of that electric current with the same proportions as the free access space.

The magnitude of the magnetic field due to current-carrying wire is,

$\mathbf{B}\mathbf{=}\frac{{\mathbf{渭}}_{\mathbf{0}}\mathbf{I}}{\mathbf{2}\mathbf{蟺谤}}$

Here, B is the magnetic field, ${\mathbf{渭}}_{\mathbf{0}}$is the permeability of free space, I is the current, and r is the radius.

The expression of force exerted by one current carrying wire on the other is,

$\mathbf{F}\mathbf{=}\frac{{\mathbf{渭}}_{\mathbf{0}}{\mathbf{L}}_{\mathbf{1}}{\mathbf{I}}_{\mathbf{2}}}{\mathbf{2}\mathbf{蟺谤}}$

Where, ${\mathbf{I}}_{\mathbf{1}}$and ${\mathbf{I}}_{\mathbf{2}}$are current and L is the length of wire.

The diagram depicting the force on one wire is given below

Apply $\underset{}{鈭�}F=0$on the wire as the current and force are inter dependent.

The force on one wire is given by,

$\mathrm{F}=\left(\frac{{\left.{\mathrm{渭}}_0鈰�\right|}^2}{2\mathrm{蟺谤}}\right)\mathrm{L}$

The distance between the wires is,

$\begin{array}{r}\mathrm{r}=2\left(0.040\mathrm{m}\right)\sin 鈦�胃\\ =8.362脳{10}^{鈭�3}\mathrm{m}\end{array}$

From the image,

$\left(\frac{{渭}_0鈰�l^2}{2蟺r}\right)L=位Lg\tan 鈦�胃$

Here,$\mathrm{m}=\mathrm{位尝}$

Solve for the current I,

$\mathrm{I}=\sqrt{\frac{\mathrm{位驳谤迟补苍}鈦�\mathrm{胃}}{\left(\frac{{\mathrm{渭}}_0}{2\mathrm{蟺}}\right)}}$ 鈥�.. (1)

Consider the given data as below.

The wires have a mass per unit length,$位=0.0125\mathrm{kg}/\mathrm{m}$

Acceleration due to gravity,$\mathrm{g}=9.80\mathrm{m}/{\mathrm{s}}^2$

Angle,$\mathrm{胃}=6.00掳$

Permeability of free space,${渭}_0=4脳{10}^{鈭�7}\mathrm{T}鈰�\mathrm{m}/\mathrm{A}$

Substitute known values into equation (1).

$\begin{array}{r}\mathrm{I}=\sqrt{\frac{(0.0125\mathrm{kg}/\mathrm{m})\left(9.80\mathrm{m}/{\mathrm{s}}^2\right)\left(\tan 鈦�{6.00}^{鈭�}\right)\left(8.362脳{10}^{鈭�3}\mathrm{m}\right)}{2脳{10}^{鈭�7}\mathrm{T}鈰�\mathrm{m}/\mathrm{A}}}\\ =23.2\mathrm{A}\end{array}$

Thus, the current in each wire is 23.2 A.