**A straight wire carries a 10.0-A current. ABCD is a rectangle with point D in the middle of a 1.10-mm segment of the w…**

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## Question “A straight wire carries a 10.0-A current. ABCD is a rectangle with point D in the middle of a 1.10-mm segment of the w…”

A straight wire carries a 10.0-A current. ABCD is a rectangle

with point D in the middle

of a 1.10-mm segment of the wire and point C in the wire. Find the

magnitude and

direction of the magnetic field due to this segment at (a) point A;

(b) point B; (c) point C.

## Answer

Biot – Savart Law is the concept that will solve the question.

First, use the Biot – Savart Law to calculate the magnetic field created by a wire carrying a current. This is the equation for magnetic field caused by a current-carrying wire.

The direction of your fingers can be used later to calculate the magnetic field’s direction. You can also repeat the process for other distances.

**Biot – Savart Law**

Biot – Savart Law explains the relationship between the magnetic field, and current carrying elements. A current carrying wire is an example. Every infinitesimal electron of current contributes to the magnetic field at P, which is perpendicular the current element. A vector product is required to calculate the magnetic field due a current element.

The following is the mathematical expression of Biot – Savart law.

denotes the magnetic field at point r,

the length of the conductor carrying the current,

the unit vector that indicates the direction of distance r from current to point, and

the permeability in free space.

You can calculate the direction of the magnetic field by using the right hand thumb rule. This involves placing your right-hand thumb in the direction that the current is going and then curling your fingers around the conductor. The direction of the magnetic fields is determined by the curled fingers.

Pythagoras’ theorem can be used to calculate distance between points. This applies to right-angled triangles.

*c* is here, while *b*, *a*, are the legs for the right-angled triangle.

(**a**)

**Direction and magnitude of the magnetic field at point A:**

Take the following expression to create a magnetic field according to Biot-Savart law.

Substitute

to

, 10 A for I and

to dl, and

to

.

The magnetic field direction at point A is not in the page.

(**b**)

**The direction and magnitude of the magnetic field at point B:**

Distance between points D and B

Substitute 5 cm *AD* for 14 cm *AB*.

The angle between the current carrying line and the line BD.

Substitute 5 cm *CB* for 0.148 m *DB*.

The magnetic field at point A,

Substitute

to

, 10 A for I and

to dl,

to

, and

to r.

The magnetic field direction at point *B* is outward.

(**c**)

**Direction and magnitude of the magnetic field at point C:**

The angle between D and C is.

The magnitude of the magnetic force at point C is thus,

Ans: Part A

The magnetic field magnitude at point A is

, and the direction moves away from the page.

## Conclusion

Above is the solution for “**A straight wire carries a 10.0-A current. ABCD is a rectangle with point D in the middle of a 1.10-mm segment of the w…**“. We hope that you find a good answer and gain the knowledge about this topic of **science**.