Electric currents and magnetic fields

Physics > Electric currents and magnetic fields

Consider electric current magnetic field… Learn how to use the Right Hand Rule, Magnetic Field in Bio-Savard’s Law, Ampere’s Law and Formula.

Electricity generates a magnetic field that can be transmitted as a series of circular field lines around the wire segment.

Learning challenge

• Describe the shape of the magnetic field formed due to the action of the current.

Key points

• The closed-line magnetic field is generated by a current-filled wire.
• The Right Hand Rule helps you calculate the direction of the magnetic field.
• Bio-Savard’s law is used to calculate the field strength. For a simple situation:
• More fundamental is Ampere’s Law, which connects the magnetic field and the flux: ∮B ⋅ dl = μ₀I_encwhere I_enc (closed current, and μ₀ – constant).
• A conductive wire perceives force in the presence of an external magnetic field: F = Bilsinθ (ℓ is the length of the wire, i is the current, and θ is the angle between the direction of the current and the magnetic field).

Terms

• Bio-Savart’s Law is an equation that characterizes the magnetic field created by the current. Associates a magnetic field with the magnitude, direction, length, and proximity of an electric current.
• Ampere’s Law is an equation that relates a magnetic field to an electric current. It can be used to determine a specific magnetic field.

Electric current and magnetic fields

A magnetic field is created by the influence of an electric current and can be visualized as circular field lines around a wire. Among the study methods, a compass is used to determine the direction of the field. There is also a rule of the right hand, where the thumb points to the direction of the current, and the fingers are clamped in the direction of the created magnetic field loops.

(a) – Compasses located near a long straight conductive wire. They demonstrate that the field lines create circular loops. (b) – Rule of the right hand: if the thumb is directed towards the current, then the fingers indicate the direction of the field

Magnetic field strength

To determine the strength of the magnetic field created by a long straight conductive wire, use the formula:

For a long straight wire, where I is the current, r is the shortest distance to the wire, and the constant 0 = 4π10^-7 T⋅m / A – free space permeability. The wire is very long, so the value will only be based on the distance from the wire.

Each segment of the current forms a magnetic field, and the total one displays the vector sum of the fields of all segments. The formal statement of the direction and magnitude of the magnetic field, taking into account each segment, is called the Bio-Savard law. To add fields for an arbitrary current, an integral calculation must be performed. The full form of Bio-Savard’s law for the magnetic field is:

(the vector dℓ is the direction of the current; R is the distance between the position dℓ and the place where the magnetic field is calculated; R is the unit vector in the direction r).

Ampere’s law

Ampere’s Law is considered a more fundamental law and relates magnetic field and flux. In units, the integral form acts as a linear integral around a closed curve C (it is limited as a surface S through which an electric current passes).

The total magnetic field around a certain path appears in direct proportion to the current passing through it. In the form of a formula, Ampere’s law:

Here the magnetic field is integrated along the curve and is equivalent to the flux density. Ampere’s Law always works for stationary currents and can be used to determine the B-field in some highly symmetric situations, such as an infinite wire or solenoid.

Force on the conductor

The force on the conducting wire is the same as the force of the moving charge. Take a conductor with a length ℓ, a cross-section A and a charge q, which is due to an electric current i. If the conductor is lowered into a magnetic field with a value of B, then the acting force on the charge is equal to:

The right hand rule determines the direction of force on a conductive wire immersed in an external magnetic field.

F = qvBsinθ

For N charges, where N = nLA, the force affecting the conductor: F = FN = qvBnlAsinθ = Bilsinθ (i = nqvA). The right hand rule indicates the direction of force on the wire, as shown in the figure. Do not forget that field B is external.

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