Question

Given a short solenoid, length 30cm,radius 15 cm ,500 turns,current 7 ampere. What is magnetic field at the end of the solenoid?

Answer 1

Expression for the magnetic field at distance D from the edge of the solenoid can be given as

$$B=\frac{\mu NI}{2}\left(\frac{D+L}{\sqrt{(D+L)^2+R^2}}-\frac{D}{\sqrt{D^2+R^2}}\right)$$

Now at the end of the solenoid D=0, so expression becomes

$$B=\frac{\mu NI}{2}\left(\frac{L}{\sqrt{(L)^2+R^2}}\right)$$

$$B=\frac{(4\pi \cdot10^{-7})(500)(7)}{2}\left(\frac{0.3}{\sqrt{(0.3)^2+0.15^2}}\right)\\=0.002\ T=2.0\ mT$$