In a uniform magnetic field, can an Amperian loop ever have a non-zero value of its line integral with the magnetic field?
a)yes
b)No, it will always be zero
c)depends on the orientation and shape of the loop.
c)depends on the orientation and shape of the loop.
c) depends on the orientation and shape of the loop.
The line integral of the magnetic field along an Amperian loop will be non-zero if the loop is not parallel to the field lines. If the loop is parallel to the field lines, the line integral will be zero because the dot product of the magnetic field and the tangent vector to the loop will be zero. However, if the loop has a component perpendicular to the field lines, the line integral will be non-zero. The magnitude of the line integral will depend on the strength of the magnetic field and the size and shape of the loop.
The correct answer is a) yes. In a uniform magnetic field, an Amperian loop can have a non-zero value of its line integral with the magnetic field.
To understand why, let's first define an Amperian loop. An Amperian loop is a closed loop in which you can imagine a current flowing through it. It is used in Ampere's Law, which relates the magnetic field along the path of the loop to the current passing through it.
Now, when a uniform magnetic field is present, the magnetic field lines are parallel and have a constant magnitude and direction. If the Amperian loop is oriented perpendicular to the magnetic field lines, the line integral of the magnetic field along the loop will be non-zero. This is because the magnetic field lines crossing the loop will have a nonzero component along the direction of the loop, resulting in a non-zero value for the line integral.
However, if the Amperian loop is oriented parallel to the magnetic field lines, the line integral of the magnetic field along the loop will be zero. This is because there is no component of the magnetic field perpendicular to the loop to contribute to the line integral.
Therefore, the value of the line integral of the magnetic field along an Amperian loop in a uniform magnetic field depends on the orientation and shape of the loop.