Question

Find the magnitude of the magnetic field ∣∣B⃗ (r)∣∣ inside the cylindrical resistor, where r is the distance from the axis of the cylinder, in terms of i, r, r0, l, and other given variables. You will also need π and μ0. Ignore fringing effects at the ends of the cylinder.

Answer 1

Answer:

The magnetic field inside the cylindrical resistor is $\dfrac{\mu_{0}ir}{2\pir_{0}^2}$

Explanation:

Given that,

Distance from the axis of the cylinder = r

We need to calculate the magnetic field inside the cylindrical resistor

Using formula of magnetic field

$\oint{\vec{B}\cdot\vec{dl}}=\mu_{0}i_{encl}$

$B\cdot(2\pi r)=\mu_{0}\dfrac{i\pir^2}{\pi r_{0}^2}$

Where, r₀ = radius

r = distance

i = current

$|\vec{B}(r)|=\dfrac{\mu_{0}ir}{2\pir_{0}^2}$

Hence, The magnetic field inside the cylindrical resistor is $\dfrac{\mu_{0}ir}{2\pir_{0}^2}$