Answer :
The points are:
(a) x = 0.500 m, y = 0, z = 0 (b) x = 0, y = 0, z = +0.500 m
Answer:
a) [tex] B = -2.38\times10^{-5} \hat k[/tex]
b) [tex] B = 2.38\times10^{-5} \hat i [/tex]
Explanation:
The magnetic field can be calculated as follows:
[tex]B= \frac{\mu_o}{4\pi}\frac{q (\vec v\times \hat r)}{r^2}[/tex]
a) The velocity vector is in +y direction and the point is on x-axis
Because [tex]\hat j \times \hat i = -\hat k[/tex],
[tex]B= \frac{\mu_o}{4\pi}\frac{q (\vec v\times \hat r)}{r^2}[/tex]
[tex]B= 1\times 10^{-7}\times 7\times 10^{-6}\times \frac{8.50\times 10^6 \hat j\times \hat i}{0.500^2}\\B = -2.38\times10^{-5} \hat k[/tex]
b) The velocity vector is in +y direction and the point is on z-axis
Because [tex]\hat j \times \hat k = \hat i[/tex],
[tex]B= \frac{\mu_o}{4\pi}\frac{q (\vec v\times \hat r)}{r^2}[/tex]
[tex]B= 1\times 10^{-7}\times 7\times 10^{-6}\times \frac{8.50\times 10^6 \hat j\times \hat k}{0.500^2}\\B = 2.38\times10^{-5} \hat i[/tex]