Complete Question
A horizontal rectangular surface has dimensions 2.50 cm by 3.50 cm and is in a uniform magnetic field that is directed at an angle of 34.5 degree above the horizontal.
What must the magnitude of the magnetic field be in order to produce a flux of 4.50×10−4 Wb through the surface? Express your answer with the appropriate units.
Answer:
The value is [tex]B = 0.908 \ T[/tex]
Explanation:
From the question we are told that
The dimension of the rectangular surface is [tex]2.50 \ cm\ (0.025 \ m ) \ by \ 3.5 \ cm\ (0.035 \ m )[/tex]
The angle is [tex]\theta = 34.5 ^o[/tex]
The magnetic flux is [tex]\phi = 4.50* 10^{-4} \ Wb[/tex]
Generally the area of the rectangular surface is
[tex]A = 0.025 * 0.035[/tex]
=> [tex]A = 0.000875 \ m^2[/tex]
Generally magnetic flux is mathematically represented as
[tex]\phi = B * A cos (90 - \theta)[/tex]
So
[tex]4.50* 10^{-4} = B * 0.000875 cos (90 - 34.5)[/tex]
=> [tex]B = \frac{4.50* 10^{-4} }{ 0.000875 cos (90 - 34.5) }[/tex]
=> [tex]B = 0.908 \ T[/tex]
