Magnetic Effects of Current and Magnetism Chapter - Physics JEE Main

JEE Main Physics Chapters 

1

Units and Measurement

11

Electrostatics

2

Kinematics

12

Current Electricity

3

Laws of Motion

13

Magnetic Effects of Current and Magnetism

4

Work, Energy and Power

14

Electromagnetic Induction and Alternating Currents

5

Rotational Motion

15

Electromagnetic Waves

6

Gravitation

16

Optics

7

Properties of Solids and Liquids

17

Dual Nature of Matter

8

Thermodynamics

18

Atoms and Nuclei

9

Kinetic Theory of Gases

19

Electronic Devices

10

Oscillations and Waves

20

Communication Systems

Name of the Concept

Key Points of Concept

1. Magnetic force on a moving charge in a magnetic field

• A moving charge produces an electric field and magnetic field.

• The charge (q) moving with a velocity (v) in a magnetic field (B) experiences a magnetic force(F) given by 

$\vec F=q(\vec v\times \vec B)$

$F=qvB\sin\theta$

• The direction of magnetic force is given by right-hand rule as shown below

2. The trajectory of a charge moving in a perpendicular magnetic field

• When a charge (q) moves in a perpendicular magnetic field (B), then it follows a circular path and necessary centripetal force is given magnetic force.

• The radius (R) of the circular path is given by

$R=\dfrac{mv}{qB}$

• Time period of motion of charge in a circular path is

$T=\dfrac{2\pi m}{qB}$

• Kinetic energy of circular path is given by

$K=\dfrac{q^2B^2R^2}{2m}$

3. Cyclotron

• Cyclotron is a device used to accelerate positively  charged particles.

• The charged particles are accelerated by an alternating electric field created by two D shaped semicircular hollow chambers in a perpendicular magnetic field.

• Since the charged particle is moving in a perpendicular magnetic field, it follows a circular path of increasing radius

• The cyclotron frequency is given by

$f=\dfrac{qB}{2\pi m}$

4. Biot Savart Law

• According to Biot Savart law, the magnetic field (dB) at a point due to the current element (dl) is given by the expression

$\vec dB=\dfrac{\mu_0}{4\pi}\dfrac{\vec {Idl}\times\vec r}{r^3}$

$dB=\dfrac{\mu_0}{4\pi}\dfrac{Idl\sin\theta}{r^2}$

Where μ is the magnetic permeability of the medium and for free space, magnetic permeability μ0 = 4ℼ✕ 10-7 H/m

• If you hold a current-carrying conductor in such a way that your thumb points towards the direction of current, then the remaining fingers give the direction of the magnetic field at that point.

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• In the case of a circular current-carrying coil, if the four folding fingers of the right-hand point towards the direction of the current, then the thumb point towards the direction of magnetic field

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5. Ampere

• The ampere (A) is the base unit of electric current in the International System of Units (SI). One ampere is defined as the constant current that, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one meter apart in a vacuum, would produce a force between them of 2 x 10⁻⁷ newtons per meter.

6. Ampere’s Law

• Ampere’s law gives a method to calculate the magnetic field due to a given current distribution.

• According to ampere’s law, the line integral of the magnetic field around any closed curve is equal to μ0 times the net current enclosed by the closed curve. 

• $\oint\vec B\cdot\vec{dl}=\mu_0i_{enclosed}$

• $\oint\vec B\cdot\vec{dl}=\mu_0(i_1+i_3-i_2)$

7. Torque Experienced by a Current Loop in a Uniform Magnetic Field

• When a current loop is placed in a uniform magnetic field, it experiences a torque according to the following formula:

τ=BIAsinθ

Where, 

τ: Torque on the current loop (in newton-meters, N·m)

B: Magnetic field strength (in teslas, T)

I: Current flowing through the loop (in amperes, A)

A: Area of the loop (in square meters, m²)

θ: Angle between the plane of the loop and the direction of the magnetic field.

8. Moving Coil Galvanometer

• A moving coil galvanometer is a device used to measure small electric currents. It consists of a coil of wire suspended in a magnetic field. When current flows through the coil, it experiences a torque, causing the coil to rotate. The deflection of the coil is proportional to the current passing through it, making it a useful instrument for current measurement.

9. Current Sensitivity and Conversion to Ammeter and Voltmeter

• The current sensitivity of a galvanometer is a measure of how much the pointer of the galvanometer deflects for a given current. To convert a galvanometer into an ammeter, a low-resistance shunt resistor is placed in parallel with the galvanometer coil. This allows the ammeter to measure higher currents while protecting the galvanometer from damage. To convert it into a voltmeter, a high-resistance resistor is connected in series with the galvanometer to measure voltage across a circuit element.

10. Magnetic field due to a circular and straight wire

• Magnetic field due to a circular coil having current I and radius R at a distance x along its axis is given by

$B=\dfrac{\mu_0IR^2}{2(R^2+x^2)^{3/2}}$

• Magnetic field due to an infinitely long current-carrying wire having current I at a distance d  is

$B=\dfrac{\mu_0I}{2\pi d}$

11. Magnetic field due to a solenoid

• A solenoid is a tightly wounded cylindrical coil of insulated wire having a smaller diameter than its length

• Magnetic field due to a solenoid having n number of turns per unit length along its axis outside the solenoid

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$B=\mu_0nI$

12. Force on a current-carrying conductor in a magnetic field.

• When a current-carrying conductor having length L is placed in a magnetic field B, it will experience a force given by the formula,

$F=ILB\sin\theta$

The direction of force is given by fleming’s left-hand rule as given below

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13. Force between two parallel current-carrying conductors

• Force  acting between two parallel current-carrying conductors having length l is given by

$F_1=\dfrac{\mu_0}{4\pi}\dfrac{2I_1I_2}{d}\times l$

$F_2=\dfrac{\mu_0}{4\pi}\dfrac{2I_1I_2}{d}\times l$

• If the current in the conductors is in the same direction, there will be the force of attraction and if the currents are in the opposite direction, then there will be the force of repulsion

14. The magnetic dipole moment of a magnet

• Magnetic dipole moment of a magnet gives the strength of a magnet. 

• It is a vector quantity directed from south to north and its magnitude is given by

$\vec M=m(2\vec l)$

Where m is the pole strength and l is the magnetic length.

15. Terms related to magnetism

• Intensity of magnetising field (H):

Intensity of magnetising field or magnetising field is the extent to which a magnetic field can magnetise a substance and its SI unit is A/m

• Intensity of Magnetisation(I):

It is the degree to which a substance is magnetised when it is placed in a magnetic field given by the formula,

$I=\dfrac{M}{V}$

Where M is the induced dipole moment and V is the volume

• Magnetic susceptibility (ꭕm)

Magnetic susceptibility of a material is defined as the ratio of the intensity of magnetisation (I) to the magnetic intensity(H) applied to the substance.

$\chi_m=\dfrac{I}{H}$

16. Magnetic Field Lines

Magnetic field lines are imaginary lines used to visualize and represent the magnetic field around a magnet or a current-carrying conductor. The key properties of magnetic field lines are:

• They form closed loops.

• They emerge from the north pole and enter the south pole of a magnet.

• They never intersect.

17. Elements of Earth’s Magnetic Field

• There are three elements used to completely determine the earth’s magnetic field at a place. They are given below

• Magnetic declination(θ): It is the angle between geographic meridian and magnetic meridian planes at a place

• Angle of inclination or dip(ɸ): It is the angle that the intensity of the magnetic field of earth makes with horizontal line.

• The horizontal component of earth’s magnetic field (BH): The earth’s magnetic field (B) at a place can be resolved into horizontal(BH) and vertical (Bv)  components.

$B_V=B\sin\phi$

$B_H=B\cos\phi$

$\tan\phi=\dfrac{B_V}{B_H}$

Where ɸ is the angle of inclination.

18. Magnetic Materials

• Paramagnetic Materials

These materials experience a weak force of  attraction in a magnetic field. They get feebly magnetised in the direction of the applied magnetic field.

Eg:- Al, Na, O2(at S.T.P)

• Diamagnetic materials

Diamagnetic materials experience a weak force of repulsion in an external magnetic field. They also get weakly magnetised in the opposite direction of the applied magnetic field.

Eg: Cu, Bi, N2(at STP), Pd

Ferromagnetic materials

These materials experience a strong force of attraction in a magnetic field. They get strongly magnetised in the direction of the applied magnetic field.

Eg: Fe, Co, Ni,

19. Magnetic Susceptibility and Permeability

• Magnetic Susceptibility (χ) is a measure of a material's ability to become magnetized when exposed to an external magnetic field. It is defined as the ratio of the induced magnetization to the applied magnetic field:

χ = M/H

• Permeability (μ) is a measure of a material's ability to conduct magnetic lines of force. It is related to magnetic susceptibility and is used to define the relationship between magnetic field strength (H) and magnetic flux density (B):

B = μH

20. Curie’s Law

• According to curie’s law, the magnetic susceptibility of a paramagnetic substance is inversely proportional to its absolute temperature.

$\chi\varpropto\dfrac{1}{T}$

$\chi=\dfrac{C}{T}$

Where C is the curie’s constant and T is the absolute temperature. 

• The temperature above which a ferromagnetic material becomes paramagnetic material is called curie temperature.

21. Hysteresis Curve

• It is a B-H curve of a ferromagnetic material by noting down the variation in magnetic field density (B) with respect to changing magnetising field (I).

• The lagging of magnetic flux density behind the magnetising field is called hysteresis and the B-H curve is called the hysteresis curve.

•  The remainder value of magnetic flux density (ob) even after magnetising field (H) is reduced to zero is called retentivity.

• The value of magnetising in the opposite direction to reduce the magnetisation of the material to zero is called coercivity

• The area of the B-H curve gives the energy loss per one cycle of magnetisation and demagnetisation.

22. Electromagnets and Permanent Magnets

• Electromagnets are temporary magnets created by passing an electric current through a coil of wire. The strength of the magnetic field can be controlled by varying the current or the number of turns in the coil.

• Permanent Magnets are materials that retain their magnetization after the magnetizing field is removed. Common examples include bar magnets and neodymium magnets.

Sl. No

Name of the Concept

Formula

1.

Lorentz force formula

The force acting on a charged particle (q) in a combined electric field (E) and magnetic field (B)

$\vec F=q\vec E+q(\vec v\times \vec B)$

2.

Pitch and radius of a helical path of a charged particle (q) moving at an angle θ to the magnetic field(B) with a velocity (v) 

$\text{Pitch}=\dfrac{2\pi mv\cos\theta}{qB}$

$r=\dfrac{mv\sin\theta}{qB}$

3.

Magnetic field inside a torroid 

$B=\mu_0nI$

4.

The magnetic moment of a current-carrying coil having an area of cross-section (A) and N number of turns

$ M=NAI$

5.

The torque acting on a current-carrying coil placed in a magnetic field B

$ \tau = NAIB\sin\theta$

Where θ is the angle between area vector and magnetic field and N is the number of turns 

7.

The torque acting on a magnetic dipole placed in a magnetic field B

$\vec \tau = \vec M\times \vec B$

$ \tau = MB\sin\theta$

Where θ is the angle between magnetic dipole moment M and magnetic field B.

7.

The potential energy of a magnetic dipole in an external magnetic field B.

$ P.E = -MB\cos\theta$

Where θ is the angle between magnetic dipole moment M and magnetic field B.

8.

Relation between relative permeability (μr) and magnetic susceptibility(𝜒m)

$\mu_r=1+\chi_m$

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