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.
The correct answer is b) No, it will always be zero.
To understand why, let's first discuss what an Amperian loop is. An Amperian loop is a closed loop that is used to apply Ampere's Law, which relates the magnetic field to the current flowing through the loop. It's a theoretical concept that helps us understand the behavior of magnetic fields.
In a uniform magnetic field, the field lines are parallel and have the same magnitude and direction throughout. When we integrate the magnetic field along an Amperian loop, the line integral gives us the total magnetic field strength multiplied by the length of the loop, as the direction of the magnetic field is always parallel to the loop.
Since the magnitude and direction of the magnetic field are the same at all points along the loop, the line integral of the magnetic field is constant throughout the loop. Therefore, the line integral of the magnetic field over the loop will always be zero, regardless of the orientation or shape of the loop. The magnetic field contribution from each segment of the loop will cancel out with the contribution from the opposite segment, resulting in a net line integral of zero.
So, choice b) No, it will always be zero, is the correct answer.