Magnetic Effects of Current and Magnetism

The One Thing

Electric currents produce magnetic fields, while magnetic fields exert forces on moving charges and current-carrying conductors. The resulting phenomena—including particle motion, motor action, electromagnetic induction, galvanometer operation, and magnetic-material behaviour—are explained by field laws, force laws, and the alignment of magnetic moments.

Reactions, Processes and Experiments

Key Terms

• Magnetic field: The region around a magnet or current-carrying conductor in which a magnetic force can be detected; its SI unit is tesla (T).
• Magnetic field lines: Imaginary lines whose tangent gives the field direction; they form closed curves and never intersect.
• Magnetic field vector $B$: A vector quantity representing magnetic field; its SI unit is tesla, with $1T=1N/(Am)$.
• Lorentz force: The force on a charged particle moving in electric and magnetic fields, given by $F=q(E+v\times B)$.
• Magnetic force on a moving charge: For charge $q$ moving with velocity $v$ in magnetic field $B$, the force magnitude is $F=qvB\sin \theta$.
• Biot–Savart law: It gives the magnetic field contribution of a small current element: $dB=({\mu }_0/4\pi )(Idl\sin \theta /r^2)$.
• Ampere’s circuital law: The line integral of magnetic field around a closed path equals ${\mu }_0$ times the enclosed current: $\oint B\cdot dl={\mu }_{0}I$.
• Right-hand thumb rule: When the right thumb points in the direction of current, the curled fingers show the direction of magnetic field around the conductor.
• Fleming’s left-hand rule: A rule used to determine the direction of magnetic force on a current-carrying conductor in a magnetic field.
• Force on a current-carrying conductor: A conductor of length vector $l$ carrying current $I$ in magnetic field $B$ experiences $F=I(l\times B)$, with magnitude $F=BIl\sin \theta$.
• Force between parallel currents: Two parallel currents in the same direction attract, while currents in opposite directions repel; $F/L={\mu }_0{I}_1{I}_2/(2\pi d)$.
• Magnetic dipole: A system with separated magnetic poles or a current loop; the magnetic dipole moment of a current loop is $m=NIA$.
• Torque on a current loop: A current loop in a uniform magnetic field experiences torque $\tau =m\times B$, with magnitude $\tau =NIAB\sin \theta$.
• Motion of a charged particle in a magnetic field: When velocity is perpendicular to the field, the particle moves in a circle of radius $r=mv/(qB)$ and angular frequency $\omega =qB/m$.
• Cyclotron: A device that accelerates charged particles using a perpendicular magnetic field and an alternating electric field; its cyclotron frequency is $f=qB/(2\pi m)$.
• Moving-coil galvanometer: An instrument that detects and measures small currents using the torque on a current-carrying coil in a magnetic field.
• Magnetic flux: The magnetic field passing through an area, given by ${\Phi }_B=BA\cos \theta$; its SI unit is weber (Wb).
• Magnetic permeability: A measure of how easily a material supports magnetic field formation, represented by $\mu$; relative permeability is ${\mu }_r=\mu /{\mu }_0$.
• Magnetisation: The magnetic dipole moment developed per unit volume of a material, represented by $M$.
• Magnetic susceptibility: The ratio of magnetisation to magnetising field, ${\chi }_m=M/H$, indicating how strongly a material responds to an applied field.
• Diamagnetic material: A material weakly repelled by a magnetic field, with small negative susceptibility; examples include copper, bismuth, and water.
• Paramagnetic material: A material weakly attracted by a magnetic field, with small positive susceptibility; examples include aluminium, platinum, and oxygen.
• Ferromagnetic material: A material strongly attracted by a magnetic field because of aligned magnetic domains; examples include iron, cobalt, and nickel.
• Magnetic domains: Small regions in a ferromagnetic material where atomic magnetic moments are aligned in the same direction.
• Hysteresis: The lag of magnetisation behind the magnetising field during repeated magnetisation and demagnetisation.
• Retentivity: The ability of a material to retain magnetisation after the external magnetic field is removed.
• Coercivity: The magnitude of reverse magnetic field required to reduce the magnetisation of a material to zero.
• Permeability of free space: ${\mu }_0=4\pi \times 10^{-7}Tm{A}^{-1}$.
• Magnetic field strength $H$: The magnetising field used to describe the magnetic response of a material.
• Magnetic induction $B$: The magnetic field quantity in a material related to $H$ and $M$ by $B={\mu }_0(H+M)$.
• Curie temperature: The temperature above which a ferromagnetic substance loses ferromagnetism and becomes paramagnetic.
• Soft magnetic material: A material with low coercivity and a narrow hysteresis loop, suitable for transformer and electromagnet cores.
• Hard magnetic material: A material with high retentivity and coercivity, suitable for permanent magnets.
• Magnetic declination: One of the magnetic elements describing the Earth’s magnetic field.
• Magnetic dip: One of the magnetic elements describing the Earth’s magnetic field.
• Horizontal component: The horizontal component of the Earth’s magnetic field.

Easily Confused

• Biot–Savart law and Ampere’s circuital law: Biot–Savart law gives the contribution from a small current element, whereas Ampere’s law relates the field around a closed path to the enclosed current and is especially useful with symmetry.
• Magnetic force and magnetic torque: Magnetic force acts on a moving charge or current-carrying conductor, whereas torque acts on a current loop or magnetic dipole and tends to align its magnetic moment with the field.
• Circular and helical motion: Circular motion occurs when velocity is perpendicular to the magnetic field; a helical path occurs when both parallel and perpendicular velocity components are present.
• Diamagnetic and paramagnetic materials: Diamagnetic materials are weakly repelled and have ${\chi }_m<0$, whereas paramagnetic materials are weakly attracted and have ${\chi }_m>0$.
• Paramagnetic and ferromagnetic materials: Paramagnetic materials are weakly attracted, whereas ferromagnetic materials are strongly attracted because of aligned magnetic domains.
• Retentivity and coercivity: Retentivity measures how much magnetisation remains after removing the external field, whereas coercivity measures the reverse field required to reduce magnetisation to zero.
• Soft and hard magnetic materials: Soft magnetic materials have low coercivity and narrow hysteresis loops, whereas hard magnetic materials have high retentivity and coercivity.
• Magnetic field $B$ and magnetising field $H$: $B$ describes magnetic induction, while $H$ describes the magnetising field; in a material they are related by $B={\mu }_0(H+M)$.
• Right-hand thumb rule and Fleming’s left-hand rule: The right-hand thumb rule gives the direction of the magnetic field around a current, whereas Fleming’s left-hand rule gives the direction of force on a current-carrying conductor.

What Gets Asked

• Field calculations for standard geometries: Questions may require $B={\mu }_{0}I/(2\pi r)$ for a long straight wire, $B={\mu }_{0}NI/(2R)$ for a circular coil, $B={\mu }_{0}nI$ for a long solenoid, or $B={\mu }_{0}NI/(2\pi r)$ inside a toroid. A common slip is applying Ampere’s law without using the symmetry appropriate to the geometry.
• Force and direction questions: Problems may use $F=qvB\sin \theta$, $F=I(l\times B)$, or the parallel-current relation $F/L={\mu }_0{I}_1{I}_2/(2\pi d)$. Marks are lost by failing to state that the force is perpendicular to both relevant directions or by reversing attraction and repulsion for parallel currents.
• Charged-particle motion: Questions may ask for the radius $r=mv/(qB)$, angular frequency $\omega =qB/m$, or cyclotron frequency $f=qB/(2\pi m)$. The key distinction is that a purely magnetic field changes the direction of motion but does no work and therefore does not change the particle’s speed.
• Current-loop and dipole calculations: Questions may require $m=NIA$, $\tau =NIAB\sin \theta$, or $U=-m\cdot B$. A frequent error is confusing magnetic dipole moment with torque or omitting the angle factor.
• Galvanometer applications: Questions may ask how a moving-coil galvanometer works, how its current sensitivity depends on $NBA/k$, or how to convert it into an ammeter or voltmeter. The specific distinction is a low-resistance shunt in parallel for an ammeter and a high resistance in series for a voltmeter.
• Classification of magnetic materials: Questions may compare diamagnetic, paramagnetic, and ferromagnetic materials using susceptibility, permeability, attraction or repulsion, and examples. Marks are lost by interchanging the signs of ${\chi }_m$, the relative permeability conditions, or the named examples.