What is the line integral of the magnetic field intensity?

What is the line integral of the magnetic field intensity?

In words, Ampère’s integral law as given by (1) requires that the line integral (circulation) of the magnetic field intensity H around a closed contour is equal to the net current passing through the surface spanning the contour plus the time rate of change of the net displacement flux density o E through the surface ( …

How do you integrate Ampere’s law?

Ampère’s law states that ∮→B⋅d→l=μ0I where I is the total current passing through the enclosed loop. The quickest way to evaluate the integral is to calculate μ0I by finding the net current through the loop. Positive currents flow with your right-hand thumb if your fingers wrap around in the direction of the loop.

What is the line integral of electric field?

The line integral of electric field around a closed loop is equal to the voltage generated in that loop (Faraday’s law): Such an integral is also used for the calculation of voltage difference since voltage is work per unit charge.

What is the integral of a vector field?

In qualitative terms, a line integral in vector calculus can be thought of as a measure of the total effect of a given tensor field along a given curve. For example, the line integral over a scalar field (rank 0 tensor) can be interpreted as the area under the field carved out by a particular curve.

What does surface integral represent?

If the vector field F represents the flow of a fluid, then the surface integral of F will represent the amount of fluid flowing through the surface (per unit time). The amount of the fluid flowing through the surface per unit time is also called the flux of fluid through the surface.

Which of the following laws states that the line integral of the magnetic field intensity around closed path is equal to the total current linked by the contour?

Ampere’s circuital law
Ampere’s circuital law: It states that line integral of the magnetic field forming a closed loop around the current (I) carrying wire, in the plane normal to the current, is equal to the μo times the net current passing through the close loop.

When the rotational path of the magnetic field intensity is zero then the current in the path will be?

The rotational path of H is zero, implies the curl of H is zero. This shows the current density J is also zero. The current is the product of the current density and area, which is also zero. 10.

What is Amperian path?

The path integral of the dot product of magnetic field and unit vector along a closed loop, Amperian loop, is proportional to the net current encircled by the loop, •A current is positive if it flows along the RHR normal direction of the Amperian loop, as defined by the direction of integration.

Is Ampere’s law a surface integral?

To apply the integral form of Ampere’s law, you need to choose an oriented surface (i.e. a surface with a choice of normal vector direction), simply because the law is stated in terms of this surface S and its boundary ∂S (which is a closed curve).

Why is the line integral of magnetic field not zero?

The integral around any closed path is zero. But →a and →b are not the same point: the path is not closed, so the integral does not have to be zero.

Why the line integral of a closed path is equal to zero?

If there is no change in magnetic flux then closed line integral of electric field is zero. Line integral of electric field gives the quantity potential difference. When we move across a loop we reach the original point having the same potential. So net potential difference is zero.

Is the line integral independent of path?

Path independence In other words, the integral of F over C depends solely on the values of G at the points r(b) and r(a), and is thus independent of the path between them. For this reason, a line integral of a conservative vector field is called path independent.

How do you find the path of a vector?

Draw a ray from the point out to infinity. Start with a count of zero. Add 1 every time a path segment crosses the ray from left to right. Subtract 1 every time a path segment crosses the ray from right to left.

What is difference between line integral and surface integral?

A line integral is an integral where the function to be integrated is evaluated along a curve and a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analog of the line integral.

What is the purpose of Amperian path in Ampere’s circuital law?

Ampere’s circuit law uses the Amperian loop to find the magnetic field in a region. The Amperian loop is one such that at each point of the loop, either: B is tangential to the loop and is a non zero constant.

What is the direction of Lorentz force?

The direction of Lorentz force is perpendicular to the direction of the moving charge and the magnetic field.