A uniform magnetic field is perpendicular to a loop of radius 1 cm. Find the value of the magnetic field such that the magnetic flux through the loop is equal to Φ0. Strategy In general, flux of a magnetic field is a scalar product of the magnetic field with the area, or Φ0 = BA cos θ, where A is

Question

A uniform magnetic field is perpendicular to a loop of radius 1 cm. Find the value of the magnetic field such that the magnetic flux through the loop is equal to [latex]\Phi_{0}[/latex].

Strategy In general, flux of a magnetic field is a scalar product of the magnetic field with the area, or [latex] \Phi_{0}=B A \cos heta[/latex], where A is the area of the loop and θ is the angle between the field vector and a vector normal to the loop. Because the magnetic field is perpendicular to the loop, [latex]\cos heta=1, ext { and so } \Phi_{0}=B A[/latex].

Accepted Answer

Solving for the magnetic field and using the given size of the loop,

[latex]\begin{aligned}B=\Phi_{0} / A &=\left(2.068 imes 10^{-15} T \cdot m ^{2} ight) /\left[\pi\left(10^{-2} m ight)^{2} ight] \&=6.58 imes 10^{-12} T\end{aligned}[/latex]

This exceptionally small value is an indication of the small size of the quantum fluxoid.

Question 10.8: A uniform magnetic field is perpendicular to a loop of radiu...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions