Verified answer

Resposta:

3) [tex]\vec{B}[/tex] = 10⁻⁵ T     e     P (•)[tex]\vec{B}[/tex]

4) [tex]\vec{B}[/tex] = 2/11 . 10⁻⁶ T

Explicação:

3)

[tex]i_{A} =10A\\\\ i_{B} =22,5A\\\\ \mu_{0} =4\pi10^{-7} \ T.m/A\\\\d_{A} =10cm=10^{-1} m\\\\d_{B} =15cm=15.10^{-2} m\\\\\\\\\vec{B}_{A}=\frac{\mu_{0}.i_{A}}{2\pi .d_{A}} \\\\\\\vec{B}_{A}=\frac{4\pi10^{-7}.10}{2\pi .10^{-1}}\\\\\\\vec{B}_{A}=\frac{2.10^{-7}.10}{10^{-1}}\\\\\\\vec{B}_{A}=2.10^{-7}.10^{2}\\\\\\\vec{B}_{A}=2.10^{-5}[/tex]

[tex]\vec{B}_{B}=\frac{\mu_{0}.i_{B}}{2\pi .d_{B}}\\\\\\\vec{B}_{B}=\frac{4\pi10^{-7} .22,5}{2\pi .15.10^{-2} }\\\\\\\vec{B}_{B}=\frac{2.10^{-7} .22,5}{15.10^{-2} }\\\\\\\vec{B}_{B}=\frac{45.10^{-7}}{15.10^{-2} }\\\\\\\vec{B}_{B}=\frac{3.10^{-7}}{10^{-2} }\\\\\\\vec{B}_{B}=3.10^{-5} \\\\\\[/tex]

[tex]\vec{B}=\vec{B}_{B}-\vec{B}_{A}\\\\\\\vec{B}=3.10^{-5} -2.10^{-5}\\\\\\\vec{B}=10^{-5}[/tex]

A direção e o sentido são influenciados pelo fio B, pois B > A.

Lembrando da Regra da Mão direita:

P (•)[tex]\vec{B}[/tex]

4)

[tex]i_{1} =i_{2} =100A=10^{2} A\\\\\mu_{0}=4\pi10^{-7}\ T.m/A\\\\d_{1}=11m\\\\d_{2}=10m[/tex]

[tex]\vec{B}_{1}=\frac{\mu_{0}.i_{1}}{2\pi.d_{1}} \\\\\\\vec{B}_{1}=\frac{4\pi10^{-7}.10^{2}}{2\pi.11} \\\\\\\vec{B}_{1}=\frac{2.10^{-7}.10^{2}}{11} \\\\\\\vec{B}_{1}=\frac{2.10^{-5}}{11} \\\\\\\vec{B}_{1}=\frac{20.10^{-6}}{11} \\\\\\\vec{B}_{1}=\frac{20}{11} .10^{-6}\ T \\\\\\[/tex]

[tex]\vec{B}_{2}=\frac{\mu_{0}.i_{2}}{2\pi.d_{2}} \\\\\\\vec{B}_{2}=\frac{4\pi10^{-7}.10^{2}}{2\pi.10} \\\\\\\vec{B}_{2}=\frac{2.10^{-7}.10^{2}}{10} \\\\\\\vec{B}_{2}=2.10^{-7}.10 \\\\\\\vec{B}_{2}=2.10^{-6}\ T \\\\\\[/tex]

[tex]\vec{B}=\vec{B}_{2}-\vec{B}_{1}\\\\\\\vec{B}=2.10^{-6} -\frac{20}{11} .10^{-6}\\\\\\\vec{B}=2.10^{-6}-1.10^{-6}-\frac{9}{11} .10^{-6}\\\\\\\vec{B}=10^{-6}-\frac{9}{11} .10^{-6}\\\\\\\vec{B}=\frac{11}{11} .10^{-6}-\frac{9}{11} .10^{-6}\\\\\\\vec{B}=\frac{11-9}{11} .10^{-6}\\\\\\\vec{B}=\frac{2}{11} .10^{-6} \ T[/tex]