Question

The circular plates of a parallel-plate capacitor have a radius of 30 mm. A steady 0.43-mA current is charging the initially uncharged capacitor, and the surface charge on the plates is distributed uniformly. The flat circular surface between the capacitor plates is coaxial and parallel to the plates, and has a radius of 13 mm. Calculate the magnetic field at any point on the circumference of the circular region (in Tesla).

Answer 1

Solution :

The electric field between two plates is given by

$E = \frac{q}{\varepsilon_0 A}$

where

$\varepsilon_0 =$ permitivity of free space

 q = charge

 A = surface area

It is given that  :

the radius of the circular plates , r = 30 mm

the current, I = 0.43 mA

Therefore, Magnetic field can be found by

$B \times 2 \pi r = \mu_0 I_{(enclosed)}$

$\Rightarrow B = \frac{\mu_0}{2 \pi r} \times (0.43 \ mA) \times \left(\frac{13 \ mm}{30 \ mm}\right)^2$

$\Rightarrow B = \frac{2 \times 10^{-7}}{13 \times 10^{-3}} \times 0.43 \times 10^{-3} \times \left(\frac{13 }{30 }\right)^2$

$\Rightarrow B = 1.2 \times 10^{-9} \ T$