TS Inter 2nd Year Physics Notes Chapter 7 Moving Charges and Magnetism

Here students can locate TS Inter 2nd Year Physics Notes 7th Lesson Moving Charges and Magnetism to prepare for their exam.

TS Inter 2nd Year Physics Notes 7th Lesson Moving Charges and Magnetism

→ Conclusion of Oersted states that moving charges produce a current and magnetic field in the surrounding space.

→ If current carrying wire is perpendicular to the plane of the paper then magnetic field lines produced are concentric circles in the plane of the paper with the conductor at centre.

→ If direction of current in a conductor is reversed then direction of magnetic field is also reversed.

→ A static charge will produce only electric field whereas a moving charge will produce both magnetic field and electric field.

→ Lorentz force: If a charge q is moving with a velocity V in electric (E̅) and magnetic fields (B) then total force on it is the sum of force due to electric field (F_ele) and force due to magnetic field (F_mag) at that given point say V.
F = q [ E(r) + v̅ × B̅ (r)] = F_ele + F_mag
This is known as Lorentz force.

→ Force acting on a current carrying conductor placed in a magnetic field F = BIf sin θ

→ Motion of a charged particle in a magnetic field : if a charged particle q’ is moving perpendicularly in a magnetic field B̅ with a velocity ‘v’ then force due to magnetic field is always perpendicular to velocity V. So it describes a circular path.
Since force and displacement are perpendicular no work is done.

→ For a charged particle moving perpendicularly in a magnetic field mv²/r = qvB. or radius of circular/ helical path r = \(\frac{m v}{q B}\)

→ Velocity selector : If a charged particle is moving in a crossed electric (E̅) and magnetic fields (B̅) such that they will cancel each other then path of charged particle is undeviated, i.e., when qE = qvB
⇒ v = \(\frac{E}{B}\)
The ratio of \(\frac{E}{B}\) for undeviation condition B is called velocity selector.

→ Cyclotron : Cyclotron is a charged particle accelerator.
Cyclotron frequency υ_c = \(\frac{\mathrm{qB}}{2 \pi \mathrm{m}}\) is independent of velocity of charged particle.

→ From Biot – Savart’s law magnetic field due to a current carrying conductor at a given point P’ is given by dB = \(\frac{\mu_0}{4 \pi} \frac{I d l \sin \theta}{\mathbf{r}^2}\)

→ From Ampere’s circuital law the total mag¬netic field coming out of a current carrying conductor is p0 times greater than the cur¬rent flowing through it.
∮B. dI = µ₀I

→ Solenoid : A solenoid consists of a long wire wound on an insulating hollow cylinder in the form of helix.
Net magnetic field is the vector sum of fields due to all turns.
Magnetic field along the axis of solenoid B= n0nI

→ Toroid : Toroid is a coiled coil.
It consists of a large number of turns of wire which are closely wound on a ring. Or Toroid is a solenoid bent into the form of a ring.
In a toroid magnetic field B = \(\frac{\mu_0 \mathrm{NI}}{2 \pi \mathrm{r}}\)
Where N = 2πrn = perimeter of toroid × number of turns per unit length.
Current loop:

→ Torque on a current loop τ = IAB sin θ
For a loop of n turns torque τ = n IAB sin θ
Here sin θ is the angle between Area vector A̅ and direction of magnetic field B̅.

→ Magnetic moment of current loop M̅ = IA̅; OR nIA̅
Torque τ = M̅ x B̅

→ For a revolving electron : Current I = e/T
Magnetic moment μ₁ = \(\frac{\mathrm{e}}{2 \mathrm{~m}_{\mathrm{e}}}\)(m_evr) = \(\frac{\mathrm{e}}{2 \mathrm{~m}_{\mathrm{e}}}\)I ;
Time period T = \(\frac{2 \pi r}{v}\)
Gyromagnetic ratio \(\frac{\mathrm{e}}{2 \mathrm{~m}_{\mathrm{e}}}\)
Angular momentum I = \(\frac{\mathrm{nh}}{2 \pi}\)

→ Moving Coil Galvanometer (M.C.G) :
Torque on the coil τ = nlAB deflection Φ = \(\left(\frac{\mathrm{NAB}}{\mathbf{k}}\right)\)I, k = torsional constant of spring.

→ To convert galvanometer into ammeter shunt to be added R_s = \(\frac{G}{n-1}\).
Where n = \(\left(\frac{i}{i_g}\right)=\frac{\text { new current }}{\text { old current }}\)
= \(\frac{\text { current to be measured }}{\text { current permitted through galvanometer }}\)

→ To convert galvanome fer into voltmeter series resistance to be added R_s = \(\frac{\mathrm{V}}{\mathrm{I}_{\mathrm{g}}}\) – R_G
Where I_g = Current permitted through galvanometer
V = Voltage to be measured.
R_G = Resistance of galvanometer.