The magnetic potential in the region in the given X v=2xy. find magnetic field at (1m, 1m)
To find the magnetic field at a given point using the magnetic potential, you can use the relationship between the magnetic potential (V) and the magnetic field (B), which is given by the equation:
B = ∇ × V
Where ∇ (del) is the gradient operator, which is a vector that represents the derivative with respect to each coordinate direction.
In this case, the magnetic potential is given as V = 2xy. To find the magnetic field at the point (1m, 1m), we need to take the gradient of V and evaluate it at that point.
Taking the gradient of V involves finding the partial derivatives of V with respect to each coordinate direction:
∂V/∂x = 2y
∂V/∂y = 2x
Now, we can evaluate the gradient vector (∇V) at the point (1m, 1m):
∇V = (∂V/∂x, ∂V/∂y) = (2y, 2x)
= (2(1m), 2(1m))
= (2m, 2m)
The magnetic field at the point (1m, 1m) is equal to the curl of the magnetic potential (∇V):
B = ∇ × V = (∂V/∂y, -∂V/∂x) = (2x, -2y)
= (2(1m), -2(1m))
= (2m, -2m)
Therefore, the magnetic field at the point (1m,1m) is given by B = (2m, -2m).