Question

Two very thick equally-magnetized square plates of side 0.25 m and of mass 21 g, are hung by threads 22.0 cm long from a common point. The plates repel and deflect from each other through a very small angle. Calculate the B field between the two plates, if the distance between them is 0.15 cm?

Answer 1

Answer:

The magnetic field between the two plates is $2.39\times10^{-4}\ T$

Explanation:

Given that,

Side of square plate = 0.25 m

Mass = 21 g

length = 22.0 cm

Distance between two plates = 0.15 cm

We need to calculate the angle

Using formula of angle

$\cos\theta=\dfrac{\dfrac{r}{2}}{l}$

Put the value into the formula

$\cos\theta=\dfrac{0.25}{2\times22.0}$

$\cos\theta=0.0056$

$\theta=\cos^{-1}(0.0056)$

$\theta=89.6^{\circ}$

From the diagram

We need to calculate the tension

Using formula of tension

$T\sin\theta=mg$

Put the value into the formula

$T=\dfrac{mg}{\sin\theta}$

$T=\dfrac{21\times10^{-3}\times9.8}{\sin89.6}$

$T=0.205\ N$

We need to calculate the magnetic force

Using formula of force

$F_{B}=T\cos\theta$

Put the value into the formula

$F_{B}=0.205\times\cos89.6$

$F_{B}=1.43\times10^{-3}\ N$

We need to calculate the magnetic field

Using formula of magnetic field

$F_{B}=\dfrac{B^2A}{2\mu}$

$B=\dfrac{F_{B}\times2\mu}{A}$

Put the value into the formula

$B=\sqrt{\dfrac{1.43\times10^{-3}\times2\times4\pi\times10^{-7}}{(0.25)^2}}$

$B=2.39\times10^{-4}\ T$

Hence, The magnetic field between the two plates is $2.39\times10^{-4}\ T$