A magnetic field has the same direction and the same magnitude B everywhere. A circular area A is bounded by a loop of wire is brought in this region. Which of the following statements is true concerning the magnitude of the magnetic flux that passes through this area?Group of answer choicesIts maximum possible value is BAIt is zero.It is BAIts minimum possible value is BA
Question
A magnetic field has the same direction and the same magnitude B everywhere. A circular area A is bounded by a loop of wire is brought in this region. Which of the following statements is true concerning the magnitude of the magnetic flux that passes through this area?Group of answer choicesIts maximum possible value is BAIt is zero.It is BAIts minimum possible value is BA
Solution
The magnetic flux through a surface is given by the dot product of the magnetic field and the area vector. The dot product takes into account the angle between the two vectors.
If the magnetic field and the area vector are parallel (i.e., the angle between them is 0 degrees), the dot product is simply the product of their magnitudes. In this case, the magnetic flux is BA.
If the magnetic field and the area vector are perpendicular (i.e., the angle between them is 90 degrees), the dot product is zero. In this case, the magnetic flux is zero.
Therefore, the magnitude of the magnetic flux that passes through the area can vary from 0 to BA, depending on the orientation of the area relative to the magnetic field. So, the statement "Its maximum possible value is BA" is true.
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