**Learning Goal: To understandAmpère’s law and its application. Ampère’s law is often written . Part A…**

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## Question “Learning Goal: To understandAmpère’s law and its application. Ampère’s law is often written . Part A…”

volume.

b) the surface integral over

theopen surface.

bounded by theloop.

integral along the closed loop.

integral from start to finish.

Part C

acircle or a sphere.

choose.

conductor.

d) over

the surface bounded by thecurrent-carrying wire.

- The path must pass through the point .
- The path must have enough symmetry so that is constant along large parts of it.
- The path must be a circle.

b) a and b

Part E

field around a straight current-carrying wire.

Part F

field at the center of a square loop carrying aconstant

current.

orfalse?

field at the center of a circle formed by acurrent-carrying

conductor.

orfalse?

field inside a toroid. (A toroid is a doughnut shapewound uniformly

with many turns of wire.)

## Answer

This problem can be solved using Ampere’s Circuital Law.

To identify the correct statements, use the Ampere circuital laws.

According to the Ampere-Circuital Law, the line integral of a magnet field along a closed loop is determined by the product of current enclosed or permeability.

This is the Ampere Circuital law.

\oint {\vec B\left( {\vec r} \right) \cdot d\vec l = {\mu _0}{I_{{\rm{encl}}}}}Here, \vec B\left( {\vec r} \right)

**(A)**

The integral is d\vec l on the left side of the ampere’s law

The integral is not found in the entire volume but only through the closed loop. It is a single integral, which means it is only line integral. It may not have a closed loop, but the line integral from beginning to end could be considered closed. It is required to be closed for Ampere law.

Accordingly, the correct statement is that integral on the left refers to the line integral running along the closed loop.

**(C)**

The integral symbol’s circle indicates that the integral is closed. This means that the integral is above a closed loop. It is possible for the loop to be any shape, and it may not have to be a circle. The path may not follow a physical conductor and is therefore arbitrary. The integral refers to length or overline, not surface.

It is therefore not above the surface of the current-carrying cable. The circle around the integral means that \vec B\left( {\vec r} \right)

**(D)**

The Ampere’s magnetic field should be along the line of integration. This is the path that must pass through point\vec r

Integration must yield a correct result if the magnetic field is sufficiently symmetric. It is impossible to integrate the discrete quantitates directly. The path must be sufficiently symmetric so that \vec B\left( {\vec r} \right) \cdot d\vec l can be integrated.

**(E)**

A symmetric closed path is possible for a straight current-carrying wire. This allows you to create a path in the plane of the cross section of the wire that encloses the current and magnet field. The circumference of the circular ring around wire can also be perpendicular to it.

Ampere’s law is a method to determine the magnetic field around a straight current-carrying cable.

**(F)**

A square closed loop has no symmetric magnetic field. It can only have one closed path through its center. Any current cannot be enclosed by the path that passes through the center of the magnetic field which is symmetric.

Ampere’s law cannot be used to locate the magnetic field in the center of a square loop that is carrying a constant current.

**(G)**

A circular closed loop has no symmetric magnetic field. It can only have one closed path through its center. Any current cannot be enclosed by the path through the center of which magnetic field is symmetric.

Ampere’s law does not allow you to locate the center of the magnetic field formed by a current-carrying conductor.

**(H)**

Toroids are doughnuts shaped with wire wound to form the doughnut’s surface. For a circular loop within a toroid, the magnetic field is constant. Also, the current contained in such a loop cannot be zero.

Ampere’s law requires that symmetric current values with lines passing through toroids be satisfied.

Ampere’s law is a method to determine the magnetic field within a toroid.

Ans Part A

The integral to the left is the line integral that crosses a closed loop.

Part C

The circle that represents the integral means that \vec B\left( {\vec r} \right)Part B

The correct statements to use are a and.

Part E

To find the magnetic field around a straight current-carrying cable, Ampere’s law is True.

Part F

You can use Ampere’s law to determine the magnetic field in the center of a square loop that carries a constant current.

Part G

To find the magnetic field center of a circle made by a current-carrying conductor, Ampere’s law is used.

Part H

To find the magnetic field within a toroid, Ampere’s law is useful.

## Conclusion

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