At a particular point on Earth, the magnitude of the Earth's magnetic field is 4.00 ✕ 10−5 T. At this point, the field through a small square loop is essentially uniform. The area of the loop is 30.0 cm2. What is the magnitude of the magnetic flux (in T · m2) through the loop when the loop is at the following orientations? (a) the magnetic field is perpendicular to the plane of the loop T · m2 (b) the magnetic field and the normal to the plane of the loop are at a 50.5° angle T · m2 (c) the magnetic field and the normal to the plane of the loop are at a 90.0° angle T · m2
First of all , we have to understand the meaning of magnetic flux ,
basically the Magnetic flux is defined as the number of magnetic field lines passing through a given closed surface. It provides the measurement of the total magnetic field that passes through a given surface area,the area under consideration can be of any size and under any orientation with respect to the direction of the magnetic field.
In order to calculate the magnetic flux, we consider the field-line image of a magnet or the system of magnets. The magnetic flux through a plane of the area given by A that is placed in a uniform magnetic field of magnitude given by B is given as the scalar product of the magnetic field and the area A. The angle at which the field lines pass through the given surface area is also important. If the field lines intersect the area at a glancing angle, that is,
- when the angle between the magnetic field vector and the area vector is nearly equal to 90ᵒ, then the resulting flux is very low.
- When the angle is equal to 0ᵒ, the resulting flux is maximum.
Hence the equation of the magnetic flux is given as the ,
where , B is the magnitude of the magnetic field and
A is the area of cross section
and is the angle made by the magnetic field vector and area vector
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