- #1

Hak

- 709

- 56

- Homework Statement
- A solenoid of length ##h## has ##N## turns. The cross-section of the solenoid is a rectangle of sides ##a## and ##b##, where ##b \ll h \ll a## (see the figure). Constant current ##I## flows in the coil wire. What is the shape of the magnetic field lines lying in the plane which is perpendicular to the sides ##a## and contains the geometrical center of the coil?

- Relevant Equations
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I was thinking of using magnetic monopoles, but I don't know how to do. I tried to calculate the magnetic flux through the cross section of the solenoid if a current ##I## flows through it. Magnetic induction inside can be given as ##B = \mu_0 n I##, whereas magnetic induction at a distance ##x## form axis is ##B = \mu_0 \frac{N}{2 \pi x} I##. So, magnetic flux through elemental strip is ##d\Phi = B h dx##. Total flux the cross section is ##\Phi = \int d\Phi = \int\frac{\mu_0 NI}{2 \pi x} h dx.## How to continue? Do you have any hints?