A magnetic field, a vector field in the vicinity of a magnet, an electric current, or a changing electric field in which magnetic forces can be observed. Magnetic fields, like those found on Earth, cause magnetic compass needles and other permanent magnets to align in the direction of the field. Magnetic fields cause electrically charged particles to move in a circular or helical pattern.
The operation of electric motors is based on this force, which is exerted on electric currents in wires in a magnetic field. The magnetic field is stationary and referred to as a magnetostatic field when it surrounds a permanent magnet or a wire carrying a steady electric current in one direction. Its magnitude and direction remain constant at any given point.
The magnetic field around an alternating current or a fluctuating direct current is constantly changing in magnitude and direction. Continuous lines of force or magnetic flux that emerge from north-seeking magnetic poles and enter south-seeking magnetic poles can be used to represent magnetic fields.
The magnitude of the magnetic field is indicated by the density of the lines. The field lines are crowded together, or denser, at the poles of a magnet, for example, where the magnetic field is strong. They fan out further away, becoming less dense as the magnetic field weakens.
Parallel straight lines with equal spacing represent a uniform magnetic field. The flux direction is the same as the direction of a small magnet’s north-seeking pole. The flux lines are continuous, forming closed loops. They emerge from the north-seeking pole of a bar magnet, fan out and around, enter the magnet at the south-seeking pole, and continue through the magnet to the north pole, where they emerge again.
The weber is the SI unit for magnetic flux. The total number of field lines that cross a given area is represented by the number of webers.
A magnetic field is a vector field that exists in the vicinity of a magnet, an electric current, or a changing electric field and can be observed to have magnetic forces. A magnetic field is created by moving electric charges and intrinsic magnetic moments of elementary particles that are associated with a fundamental quantum property known as spin.
Magnetic and electric fields are inextricably linked and both components of the electromagnetic force, one of nature’s four fundamental forces.
The magnetic field, a fundamental concept in electromagnetism, represents the region around a magnet where magnetic forces are observable. It is denoted by B and measured in Tesla (T) in the SI system. The dimensional formula of the magnetic field is derived from its definition: B=F/(q⋅v), where F is force, q is charge, and v is velocity. Substituting the dimensional formulas, we get [B]=[M1L0T^−2]/([A1T1])=[M1T^−2A^−1]. This means the magnetic field's dimensions depend on mass (M), time (T), and electric current (A).
Understanding this dimensional analysis is critical for physics students, as it not only simplifies complex electromagnetic equations but also helps verify the correctness of derived relations. Additionally, magnetic fields play a crucial role in various phenomena, from the functioning of electric motors to Earth's geomagnetic properties, making this topic essential for both theoretical and practical exam questions.
Magnetic Field’s dimensional formula is given by, M1 T-2 I-1
Where,
M = Mass I = Current L = Length T = Time Derivation
Lorentz Force (F) = Charge × Magnetic Field (B) × Velocity
Magnetic Field (B) = Lorentz Force × [Charge × Velocity]-1 . . . . . (1)
Velocity = Distance × Time-1
The velocity dimensional formula = [L T-1]. . . . . . . (2)
electric charge = electric current × time
The electric charge dimensional formula = [I1 T1] . . . . . (3)
Lorentz Force = Mass × Acceleration = M × [L T-2]
Lorentz Force Dimensional Formula = M1 L1 T-2 . . . . (4)
When we substitute equations (2), (3), and (4) into equation (1), we get
Magnetic Field = Force × [Charge × Velocity]-1
Or, B = [M1 L1 T-2] × [I1 T1]-1 × [L T-1]-1 = [M1 L0 T-2 I-1].
As a result, the Magnetic Field is dimensionally represented as [M1 T-2 I-1].
The dimensional formula of a magnetic field is derived based on the physical quantities it depends on. Magnetic field strength (B) is expressed in terms of force, current, and length, as seen in the Lorentz force equation: F=qvBsinθ, where F is force, q is charge, v is velocity, and B is the magnetic field.
Charge (q) is expressed as current×time, and velocity (v) is length per unit time. Substituting these dimensions, [B] can be deduced as [MT−2I−1], where M represents mass, T is time, and I is current. This dimensional formula helps establish a foundational understanding of the relationships magnetic fields share with other physical quantities.
The importance of the dimensions of a magnetic field lies in their ability to validate equations, analyze unit conversions, and understand the physical significance of magnetic interactions. Dimensional analysis ensures that magnetic field-related formulas are consistent and applicable in different contexts.
It aids in bridging theoretical and experimental physics by verifying the correctness of derived expressions. Additionally, understanding the dimensions enables scientists and engineers to measure and compare magnetic field strengths accurately, whether in laboratories or practical applications like electromagnets and medical imaging systems.
The applications of magnetic field dimensions span across various fields, including engineering, technology, and medicine. Magnetic field measurements are crucial for designing electrical devices like transformers, motors, and generators. In healthcare, technologies such as MRI (Magnetic Resonance Imaging) depend on precise magnetic field dimensions for diagnostic imaging.
Furthermore, the study of magnetic fields is essential in geophysics for understanding Earth’s magnetosphere, which protects against solar radiation. Space exploration, data storage in magnetic disks, and particle accelerators also rely on accurate application of magnetic field dimensions for their functionality and development.
These dimensions bridge theoretical knowledge with practical innovations, driving progress across industries.
The magnetic field of the Earth is created deep within the Earth’s core. The flow of liquid iron at the Earth’s core generates an electric current, which generates magnetic fields. Charged metals passing through these fields generate their own electric currents, and the cycle continues. The geodynamo is the name given to this self-sustaining loop. The Coriolis force causes spiralling, which aligns separate magnetic fields in the same direction. The combined effect of magnetic fields creates a massive magnetic field that engulfs the planet.