Answer to Question #103951 in Electricity and Magnetism for Dushan Madushanka

Question

L=100mm
R=100mm
I=100A

Answer 1

Let's clarify the condition. So, we have

The current $I=100A$ flows along the solenoid of length $L=100 mm$ and radius $R=100 mm$ . Find the induction of the magnetic field in the center of the solenoid. The number of solenoid turns $N=100$ and $\mu =1$.

$B=\frac {\mu \mu_0IN}{2L}(\cos \alpha_2-\cos \alpha_1)$

$\cos \alpha_1=\cos(90°+45°)=-\sin 45°=-\frac{R}{\sqrt{R^2+R^2}}=-\frac{1}{\sqrt{2}}$

$\cos \alpha_2=\cos(45°)=\frac{1}{\sqrt{2}}$

$B=\frac {\mu \mu_0IN}{2L}(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}})=$

$=\frac {1\cdot 4\cdot 3.14 \cdot 10^{-7}\cdot 100\cdot 100}{2\cdot 100}(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}})\approx9\cdot10^{-5} T$