Combined Electric and Magnetic Fields

Whenever electric and magnetic fields act on a moving charge, the charge feels a force known as Lorentz Force, a scalar quantity of forces owing to electromagnetic fields. When the electromagnetic field, magnetic Force, and charge motion are mutually perpendicular to one another, they are crossed fields, and forces owing to electric and magnetic fields operate in opposing directions. 

Magnetic Fields

• The electrical charge particle generates an electric field perpendicular to the magnetic fields. The electric field is measured in volts per metre and is a dimensionless number. We also know that the electromagnetic current is inherently conservative.
• The magnetic field is the area surrounding a magnet where the magnetic force may be seen. The flow of electric charges creates this field. As a result, magnetic fields connect the magnetic lane’s direction. The electric fields are formed around the molecules, which are distinguished by their electric charges.
• The force produced by an electric field is far greater than the force produced by a magnetic field. The circling motion of particles in a permanent magnet is used to calculate an atom’s mass. Magnetic field lines create a closed-loop, but electric field lines do not form a loop.
• All charged particles use the Lorentz force to interact with electric radiation. Electrons in a magnetic field journey in a corkscrew pattern as a result of this interaction. According to special relativity, electrons should revolve with a single frequency around the conductive direction, known as the cyclotron resonance.

As a result, the Lorentz force F will be:

F = qEî+ (qvî x Bk^) = qE – qVBî = q(E – vB) When the intensity of the electric and magnetic fields is modified to equalise the forces due to the electric and magnetic fields (FE = FB), the charge can move freely in the field.  ∴ v = E/B

This exceptional situation is employed when charged particles with a specific velocity selector (of value E/B) must pass through the crossing fields undeflected, and this phenomenon is known as a frequency selector. In 1897, JJ. Thomson used it to calculate the charge-to-mass ratio.

This velocity selector principle is also utilised in mass spectrometers to identify charged particles based on their charge to mass ratio. Velocity selector is the region to find magnetic and uniform fields. 

Solenoid Magnetic Field

A solenoid magnetic field is a wire coil that is intended to create a strong magnetic field inside it. When an electric current is fed via a wire that has been wrapped several times around a cylinder, it produces a powerful magnetic field. The magnetic field becomes stronger as the number of loops increases. The number N specifies the number of revolutions of the solenoid.

A solenoid magnetic field is a type of electromagnet designed to generate a regulated magnetic field. If the objective of a solenoid is to obstruct changes in electric current, it is characterised as an inductor.

The magnetic field of a solenoid may be calculated using the formula,

• μoIN / L = B
• Where N denotes the number of turns in the solenoid.
• I denote the coil’s current.
• L is the coil’s length.

Please keep in mind that the magnetic field in the coil is equal to μo  times the supplied current as well as the inductance per unit length.

Solved Examples 1

Determine the magnetic field created by an 80-cm-long solenoid with 360 coil turns and a current of 15 amps flowing through it.

Solution:

Given:

• N = 360 (number of turns).
• I = 15 A current

μo= 1.26 107 T/m permeability

• L = 0.8 m in length

In a solenoid formula, the magnetic field is given by,

• μoIN / L = B
• B = (1.26109 15 x 360) / 0.8
• B = 8.505104 N/Amps m
• The solenoid generates a magnetic field of 8.505104 N/Amps m.

Example 2 A 40 cm diameter solenoid has a magnetic field of 2.9105 N/Amps m. Calculate the current that passes through it if it has 300 turns.

• N = 300 turns are the solution.
• L = 0.4 m in length
• B = 2.9105 N/Amps m magnetic field.

The magnetic field formula is as follows:

• μoIN /L = B
• The current passing through the coil is denoted by
• I= BL / μoN
• I = (2.9105 x 0.4) / (1.26107 x300).
• 306 mA = I

The magnetic field inside a solenoid is a tightly coiled helical coil of wire with a tiny diameter relative to its length. The magnetic field created in the core of a current-carrying solenoid is virtually homogenous and oriented along the solenoid’s axis.

The magnetic field is much weaker outside of the solenoid. The solenoid is made of a single helical wire that carries an electric current I. The wrapping is sufficiently tight that each turn of the solenoid may be approximated as a circular wire loop located in the plane perpendicular to the solenoid’s axis and carrying a current I.

Force On a Current-Carrying Conductor in A Magnetic Field.

Theory

A current-carrying conductor in a magnetic field feels a force. If the ground and current directions are perpendicular to one another, then the resultant force on the conductor will be perpendicular to both using Fleming’s rule.

When current flows through a conductor, it is displaced, indicating the presence of a force on the conductor.

Fleming’s Left-Hand Rule: Make a straight angle with your thumb and the first two fingers on your left hand. The thumb will point in the direction of Force if the forefinger points in the direction of the field and the second finger in the direction of the Current.

Conclusion

Charged particles have long been known to travel in circular orbits under a magnetic field. Magnetic fields are also utilised in accelerators for both scientific and medicinal applications to direct the travel of charged particles. Velocity selector is the region to find magnetic and uniform fields. The circling motion of charges in a magnetic field is used to calculate an atom’s mass.