Current carrying conductor in a uniform magnetic field

Magnetic Field

A magnetic field is a vector field that describes the magnetic effect on moving electric charges, electric currents and magnetic substances. A mobile charge in a magnetic field experiences a force perpendicular to the velocity of the mobile charge and to the magnetic field.

 A permanent magnet’s magnetic field pulls on ferromagnetic substances along with iron, and attracts or repels different magnets. In addition, a magnetic field that varies with area will exert a force on a variety of non-magnetic substances through affecting the movement in their outer atomic electrons. Magnetic fields surround magnetised substances, and are created by electric powered currents along with the ones utilised in electromagnets, and by electric powered fields varying in time.

Units of Magnetic Field

The SI unit for magnetic field is Tesla (T). It is derived from the magnetic part of Lorentz force law,

Fmagnetic=q(v×B)

Where

q is the charge

v is velocity

B is magnetic field

Fleming’s Left-Hand Rule

It is observed that each time a current carrying conductor is positioned in a magnetic field, a force acts at the conductor, in a path perpendicular to both the paths of the current and the magnetic field.

Let us assume a part of a conductor of length ‘L’ is located vertically in a uniform horizontal magnetic field of strength ‘B’, produced due to magnetic poles N and S. If the current ‘I’ is flowing via this conductor, the value of the force experienced by the conductor is:

F=I(L×B)

Hold out your left hand with the forefinger, 2nd finger and thumb at a right angle to one another. If the forefinger represents the path of the magnetic field and the 2nd finger represents that of the current, then the thumb shows the path of the force.

While current flows via a conductor, one magnetic field is caused around it. The magnetic field may be imagined through taking into consideration the numbers of closed magnetic lines of force across the conductor. 

The path of magnetic lines of force may be decided by means of Maxwell’s corkscrew rule or right-hand grip rule. As consistent with those rules, the path of the magnetic lines of force (or flux strains) is clockwise if the current is flowing away from the viewer, i.e if the path of current via the conductor is inward from the reference plane.

Flux

Flux is found in electric as well as magnetic fields. It is the current induced that opposes the magnetic or electric field. Flux is an idea in implemented arithmetic and vector calculus that has many applications to physics. For delivery phenomena, flux is a vector amount, describing the value and path of the flow of a property or substance.

Magnetic Flux

Magnetic flux refers to the number of magnetic field lines passing through a closed surface. Its SI unit is – Weber.

Magnetic force in current carrying conductor derivation

We can expand the evaluation for force because of the magnetic field on a single charge to a straight rod carrying current. Consider a rod of a uniform cross-sectional area A and length l. We shall anticipate one kind of mobile carrier as in a conductor (right here electrons). Let the number density of those cell charge carriers in it be n. Then the total number of mobile charge carriers in it is nIA. For a consistent current I in this conducting rod, we might also additionally anticipate that each mobile carrier has an average drift velocity vd .

In the presence of an external magnetic field B, the force on these carriers will be,

F=(nlA)qvd×B

q= value of the charge on the carrier

 nqvd=current density j

A= cross-sectional area of the wire

Therefore,

F=[(nqvd)lA]×B=[jAl]×B

F=Il×B………..(1)

Here, l is the length of the rod, having a direction similar to current I .

Equation (1) holds for a straight rod. In this equation, B is the external magnetic field. It is not the field produced with the aid of using the current-carrying rod. If the wire has an arbitrary form we will calculate the Lorentz force on it with the aid of using taking into consideration it as a group of linear strips dl  and summing

F=ΣIdl×B

The above summation may be converted to an integral in many cases.

Conclusion

The magnetic force on a current carrying conductor in a uniform magnetic field is given by 

F=ILB sinθ

I= current flowing in the conductor

 L= length of the conductor

 B= magnitude of the uniform magnetic field

The direction of the magnetic force on a current carrying conductor in a uniform magnetic field can be derived using Fleming’s Left-Hand Rule.