Answer:
The magnetic field between the two plates is [tex]2.39\times10^{-4}\ T[/tex]
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
[tex]\cos\theta=\dfrac{\dfrac{r}{2}}{l}[/tex]
Put the value into the formula
[tex]\cos\theta=\dfrac{0.25}{2\times22.0}[/tex]
[tex]\cos\theta=0.0056[/tex]
[tex]\theta=\cos^{-1}(0.0056)[/tex]
[tex]\theta=89.6^{\circ}[/tex]
From the diagram
We need to calculate the tension
Using formula of tension
[tex]T\sin\theta=mg[/tex]
Put the value into the formula
[tex]T=\dfrac{mg}{\sin\theta}[/tex]
[tex]T=\dfrac{21\times10^{-3}\times9.8}{\sin89.6}[/tex]
[tex]T=0.205\ N[/tex]
We need to calculate the magnetic force
Using formula of force
[tex]F_{B}=T\cos\theta[/tex]
Put the value into the formula
[tex]F_{B}=0.205\times\cos89.6[/tex]
[tex]F_{B}=1.43\times10^{-3}\ N[/tex]
We need to calculate the magnetic field
Using formula of magnetic field
[tex]F_{B}=\dfrac{B^2A}{2\mu}[/tex]
[tex]B=\dfrac{F_{B}\times2\mu}{A}[/tex]
Put the value into the formula
[tex]B=\sqrt{\dfrac{1.43\times10^{-3}\times2\times4\pi\times10^{-7}}{(0.25)^2}}[/tex]
[tex]B=2.39\times10^{-4}\ T[/tex]
Hence, The magnetic field between the two plates is [tex]2.39\times10^{-4}\ T[/tex]
