Physics · Class 12 Science
Ch 10Magnetic Fields due to Electric Current — Class 12 Physics, concept-first.
Class XI's study of magnetism began with the bar magnet as a given object -- something with a fixed North and South pole whose field could be measured and drawn. This chapter turns that story on its head: instead of taking a magnet as the starting point, it asks where magnetic fields actually come from, and the answer,…
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Magnetic Field at the Centre of a Circular Current Loop
Applying the Biot-Savart law to a circular arc of wire exploits a special geometric fact unique to circles: every current element along the arc is always exactly perpendicular to the radius vector drawn to the centre, an…
Most relevant Q&A
- A conductor has 3 segments: two straight segments, each of length L, and a semicircular segment of radius R, joined so that the semicircle's…Free
- The magnetic field at the centre of a circular current-carrying loop of radius 12.3 cm is $6.4\times10^{-6}$ T. What will be the magnetic mo…Preview
- A circular coil of wire is made up of 100 turns, each of radius 8.0 cm. If a current of 0.40 A passes through it, what will be the magnetic…Preview
- A wire loop of the form shown in the figure carries a current I. Obtain the magnitude and direction of the magnetic field at P. (Given a for…Preview
- A circular coil of wire is made up of 200 turns, each of radius 10 cm. If a current of 0.5A passes through it, what will be the magnetic fie…Preview
In previous exams
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Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
Class XI's study of magnetism began with the bar magnet as a given object -- something with a fixed North and South pole whose field could be measured and drawn.
Magnetic Force
The two-wire demonstration of Section 10.1 shows that a current-carrying wire experiences a force when placed in the magnetic field produced by a neighbouring current-carrying wire.
Cyclotron Motion
A key structural consequence of Section 10.2 is that the magnetic force on a moving charge is always perpendicular to its velocity, and always has a constant magnitude for a fixed speed and field stre…
Cyclotron Accelerator
Particle accelerators -- machines that use electric and/or magnetic fields to bring charged particles up to very high energies (from a few MeV to several GeV) -- are essential tools both for fundament…
Helical Motion
Sections 10.2 and 10.3 assumed the charged particle's entire velocity lies in a plane PERPENDICULAR to the magnetic field , producing pure circular motion.
Magnetic Force on a Wire Carrying a Current
Sections 10.2 through 10.4 dealt with the magnetic force on a SINGLE moving charge. But an electric current in a wire is, physically, an enormous number of individual charge carriers (conduction elect…
Straight Wire
Consider a straight wire of length (Fig. 10.8), carrying a steady current , placed in an external magnetic field applied perpendicular to the wire.
Arbitrarily Shaped Wire
The straight-wire result of Section 10.5.1, , applies directly only when the current-carrying conductor is itself perfectly straight.
Force on a Closed Circuit in a Magnetic Field B
Section 10.5.2 established that, for a wire of arbitrary shape in a UNIFORM magnetic field, the total force depends only on the vector displacement between the wire's two endpoints.
Torque on a Current Loop
Section 10.6 showed that a current loop in a UNIFORM magnetic field experiences zero net force, but can still experience a net TORQUE, since different segments of the loop experience forces acting alo…
Moving Coil Galvanometer
A direct and historically important practical application of the torque formula (Section 10.7) is the moving coil galvanometer -- an instrument for measuring small electric currents (or, with an appro…
Magnetic Dipole Moment
Section 10.7 derived the torque on a current-carrying coil in the compact form . This particular combination of quantities, , recurs so often, and plays such a central organising role, that it is give…
Magnetic Potential Energy of a Dipole
Section 10.8 established a direct structural analogy between a magnetic dipole's torque, , and an electric dipole's torque, (from Class XI). That same analogy extends naturally to POTENTIAL ENERGY.
Magnetic Field due to a Current: Biot-Savart Law
Sections 10.1 through 10.9 dealt entirely with the FIRST half of this chapter's subject: given a magnetic field, what force (and torque) does it exert on a moving charge or a current? The remaining se…
Magnetic Field due to a Long Straight Wire
As the first, and most basic, application of the Biot-Savart law, consider a long straight wire carrying current , and a point P at perpendicular distance from the wire (Fig. 10.16).
Force of Attraction between two Long Parallel Wires
The two-wire demonstration that opened this chapter (Fig. 10.1, Section 10.1) showed QUALITATIVELY that current-carrying wires exert forces on one another -- attractive for parallel currents, repulsiv…
Magnetic Field Produced by a Current in a Circular Arc of a Wire
Having worked out the field of a straight wire (Section 10.10.1), the next natural shape to consider is a CIRCULAR arc of wire -- and, as a special case, a complete circular loop, which turns out to b…
Axial Magnetic Field Produced by Current in a Circular Loop
Section 10.12 found the field only at the CENTRE of a circular current loop. This section generalises that result to any point P on the loop's AXIS -- the straight line through the centre of the loop,…
Magnetic Lines for a Current Loop
Building directly on the on-axis field formula of Section 10.13, this section examines the overall SHAPE of the magnetic field lines produced by a circular current loop, and shows that -- viewed from…
Ampere's Law
The Biot-Savart law (Section 10.10) is completely general -- it can, in principle, be used to find the magnetic field of ANY current distribution, however complicated -- but, as the sometimes-lengthy…
Magnetic Field of a Solenoid and a Toroid
Having established Ampere's law and demonstrated its power on the simplest possible case (a single long straight wire, Section 10.15), this section turns to two more elaborate, but practically very im…
Solenoid
Consider a long, closely-wound helical coil of conducting wire -- a SOLENOID -- with its diameter assumed much smaller than its length (Fig. 10.24).
Toroid
A TOROID can be thought of as a solenoid of finite length, bent around and joined into a closed, hollow, ring- or tube-shaped structure -- similar in overall shape to a pressurised inner tube inside a…
Sample & Board Papers
Sample papers and previous-year board questions for this subject.
+−Show 21 questionsHide questions21 questions
- Q1Draw a neat labelled diagram for the construction of a 'cyclotron'.Preview
- Q2Explain how moving coil galvanometer is converted into a voltmeter. Derive the necessary formula.Preview
- Q3A rectangular coil of a moving coil galvanometer contains 100 turns, each having area 15 cm². It is suspended in the radial magnetic field 0…Preview
- Q4State and explain Ampere's circuital law.Preview
- Q5In a cyclotron, magnetic field of 1.4 Wb/m$^2$ is used. To accelerate protons, how rapidly should the electric field between the Dees be rev…Preview
- Q6A cyclotron is used to accelerate protons to a kinetic energy of 5 MeV. If the strength of magnetic field in the cyclotron is 2 T, find the…Preview
- Q7Derive an expression for magnitude of magnetic dipole moment of a revolving electron. A circular coil of 300 turns and diameter 14 cm carrie…Preview
- Q8The unit $Wbm^{-2}$ is equal to _____. (a) henry (b) watt (c) dyne (d) teslaPreview
- Q9Calculate the value of magnetic field at a distance of 3 cm from a very long, straight wire carrying a current of 6A.Preview
- Q10What is the value of force on a closed circuit in a magnetic field?Preview
- Q11Obtain an expression for magnetic induction of a toroid of 'N' turns about an axis passing through its centre and perpendicular to its plane…Preview
- Q12Calculate the current flowing through two long parallel wires carrying equal currents and separated by a distance of 1.35 cm experiencing a…Preview
- Q13Write the formula for torque acting on rotating current carrying coil in terms of magnetic dipole moment, in vector form.Preview
- Q14Explain Biot-Savart law.Preview
- Q15A circular coil of wire is made up of 200 turns, each of radius 10 cm. If a current of 0.5A passes through it, what will be the magnetic fie…Preview
- Q16What is the work done by an external uniform magnetic field perpendicular to the velocity of a moving charge?Preview
- Q17State the formula for magnetic induction produced by a current in a circular arc of a wire. Hence find the magnetic induction at the centre…Preview
- Q18A solenoid of length π m and 5 cm in diameter has a winding of 1000 turns and carries a current of 5A. Calculate the magnetic field at its c…Preview
- Q19Calculate the magnitude of force experienced by a stationary charge exposed to uniform magnetic field.Preview
- Q20Derive an expression for the magnetic field produced by a current in a circular arc of a wire using Biot-Savart law.Preview
- Q21A coaxial cable consists of a central conducting core wire of radius 'a' and a coaxial cylindrical outer conductor of radius 'b'. The two co…Preview
More questions
25 Q+−Show 5 questionsHide questions5 questions
- Q1A conductor has 3 segments: two straight segments, each of length L, and a semicircular segment of radius R, joined so that the semicircle's…Free
- Q2Figures (a) and (b) show two Amperian loops associated with conductors carrying a current I in the sense shown. The line integral (closed lo…Free
- Q3A proton enters a perpendicular uniform magnetic field B at the origin along the positive x axis with a velocity v, as shown in the figure.…Preview
- Q4A conducting thick copper rod of length 1 m carries a current of 15 A and is located on the Earth's equator, where the magnetic flux lines o…Preview
- Q5A charged particle is in motion with an initial velocity v when it enters a region of uniform magnetic field perpendicular to v. Because of…Preview
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- Q6A piece of straight wire has mass 20 g and length 1 m. It is to be levitated using a current of 1 A flowing through it and a perpendicular m…Free
- Q7Calculate the value of the magnetic field at a distance of 2 cm from a very long straight wire carrying a current of 5 A. (Given: $\mu_0=4\p…Free
- Q8An electron is moving with a speed of $3.2\times10^7$ m/s in a magnetic field of $6.00\times10^{-4}$ T perpendicular to its path. What will…Free
- Q9An alpha particle (the nucleus of a helium atom, with charge $+2e$) is accelerated and moves in a vacuum tube with kinetic energy $=10.00$ M…Preview
- Q10Two wires shown in the figure are connected in a series circuit and the same amount of current, 10 A, passes through both, but in opposite d…Preview
- Q11A very long straight wire carries a current of 5.2 A. What is the magnitude of the magnetic field at a distance of 3.1 cm from the wire? [$\…Preview
- Q12Currents of equal magnitude flow through two long parallel wires having a separation of 1.35 cm. If the force per unit length on each of the…Preview
- Q13The magnetic field at a distance of 2.4 cm from a long straight wire is $16\ \mu$T. What must be the current through the wire?Preview
- Q14The magnetic field at the centre of a circular current-carrying loop of radius 12.3 cm is $6.4\times10^{-6}$ T. What will be the magnetic mo…Preview
- Q15A circular loop of radius 9.7 cm carries a current of 2.3 A. Obtain the magnitude of the magnetic field (a) at the centre of the loop, and (…Preview
- Q16A circular coil of wire is made up of 100 turns, each of radius 8.0 cm. If a current of 0.40 A passes through it, what will be the magnetic…Preview
- Q17For proton acceleration, a cyclotron is used in which a magnetic field of 1.4 Wb/m$^2$ is applied. Find the time period for reversing the el…Preview
- Q18A moving coil galvanometer has been fitted with a rectangular coil having 50 turns and dimensions 5 cm $\times$ 3 cm. The radial magnetic fi…Preview
- Q19A solenoid of length $\pi$ m and 5 cm in diameter has a winding of 1000 turns and carries a current of 5 A. Calculate the magnetic field at…Preview
- Q20A toroid of narrow radius 10 cm has 1000 turns of wire. For a magnetic field of $5\times10^{-2}$ T along its axis, how much current is requi…Preview
- Q21In a cyclotron, protons are to be accelerated. The radius of its D is 60 cm and its oscillator frequency is 10 MHz. What will be the kinetic…Preview
- Q22A wire loop of the form shown in the figure carries a current I. Obtain the magnitude and direction of the magnetic field at P. (Given a for…Preview
- Q23Two long parallel wires, both going into the plane of the paper, are separated by a distance R and carry a current I each, in the same direc…Preview
- Q24The figure shows a section of a very long cylindrical wire of radius a, carrying a current I. The current density, which is directed along t…Preview
- Q25In the above problem, what will be the magnetic field B inside the wire at a distance r from its axis, if the current density J is uniform a…Preview