Question

Two long, parallel conductors, separated by 11.0 cm, carry currents in the same direction. The first wire carries a current I₁ = 3.00 A, and the second carries I₂ = 8.00 A. (See figure below. Assume the conductors lie in the plane of the page.)

(a) What is the magnetic field created by I₁ at the location of I₂?

magnitude	T
direction	---Select--- in the +x direction in the -x direction in the +y direction in the -y direction in the +z direction in the -z direction

(b) What is the force per unit length exerted by I₁ on I₂?

magnitude	N
direction	---Select--- in the +x direction in the -x direction in the +y direction in the -y direction in the +z direction in the -z direction

(c) What is the magnetic field created by I₂ at the location of I₁?

magnitude	T
direction	---Select--- in the +x direction in the -x direction in the +y direction in the -y direction in the +z direction in the -z direction

(d) What is the force per length exerted by I₂ on I₁?

magnitude	N
direction	---Select--- in the +x direction in the -x direction in the +y direction in the -y direction in the +z direction in the -z direction

Answer 1

Concepts and reason

The concepts used to solve this problem are magnetic field due to the straight current-carrying conductor and Fleming's left hand rule.

Use the concept of magnetic field due to the straight current-carrying conductor and Fleming’s left hand rule to determine the magnetic field and direction created by current at the location of current and also for current at the location of current .

Use the magnitude of magnetic field, length of the conductor, and current to find the to determine the force and direction exerted per unit length by current on current and also force and direction exerted per unit length by current on current .

Fundamentals

The expression for the magnetic field due to the straight current-carrying conductor is as follows:

Here, the distance between the conductor is , the current carried by the conductor is , and the permeability of the free space is .

The direction of the magnetic force can be found using the Fleming’s left-hand rule. Fleming’s left-hand rule states that “If the thumb, the index finger and the middle finger is held is such a way that all three fingers are mutually perpendicular to each other, then the thumb points in the direction of magnetic force, the index finger points in the direction of magnetic field and the thumb points in the direction of the velocity or current”.

The expression of force from Fleming's left hand rule is,

Here, is the force, is the magnitude of magnetic field, is the current, and is the length of the conductor.

(a)

Write the expression for the magnetic field created by current at the location of current as follows:

Here, the current carried by the first conductor is .

Here, the permeability of the free space is .

Substitute for , for , and for in the above expression.

The magnetic field created by current at the location of current is positive.

So,

According to Fleming’s left hand rule,

The direction of the magnetic field is in the positive z-direction.

(b)

Write the expression for the force exerted per unit length by current on current as follows:

Substitute for , for , and for in the above expression.

According to Fleming’s left hand rule,

The direction of the force is in the negative y-direction.

(c)

Write the expression for the magnetic field created by current at the location of current as follows:

Here, the current carried by the second conductor is .

Here, the permeability of the free space is .

Substitute for , for , and for in the above expression.

The direction of the magnetic field is in the negative z-direction using the Fleming’s left hand rule.

(d)

Write the expression for the force exerted per unit length by current on current as follows:

Substitute for , for , and for in the above expression.

The direction of the force is in the positive y-direction using the Fleming’s left hand rule.

Ans: Part a

The magnetic field created by current at the location of current is , and the direction of the magnetic field is in the positive z-direction.

Part b

The force exerted per unit length by current on current is , and the direction of the force is in the negative y-direction.

Part c

The magnetic field created by current at the location of current is , and the direction of the magnetic field is in the negative z-direction.

Part d

The force exerted per unit length by current on current is , and the direction of the force is in the positive y-direction.