करंट और चुंबकत्व के चुंबकीय प्रभाव (Magnetic Effects of Current and Magnetism)
In Class 12 Physics, "Moving Charges and Magnetism" provides an authoritative, curriculum-verified master resource aligned with the 2026–27 NCERT syllabus.
How do massive particle colliders at CERN accelerate protons to 99.999999% the speed of light and steer them into microscopic collisions using magnetic fields? The Lorentz Force and Biot-Savart Law govern electromagnetic dynamics.
यह अध्याय क्यों महत्वपूर्ण है
In Class 12 Physics, "Moving Charges and Magnetism" provides an authoritative, curriculum-verified master resource aligned with the 2026–27 NCERT syllabus.
अध्ययन से पूर्व (आवश्यक ज्ञान)
Electric current and magnetic field from Class 10.
Vectors and cross products.
Circular motion.
इस अध्याय के लक्ष्य
State Lorentz Force: $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$ and analyze helical trajectory in magnetic fields.
State Biot-Savart Law: $d\vec{B} = \frac{\mu_0}{4\pi}\frac{I(d\vec{l} \times \hat{r})}{r^2}$; derive field on the axis of a circular current loop.
State Ampere's Circuital Law: $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enclosed}}$ and find field inside a long Solenoid ($B = \mu_0 n I$).
Derive force between two parallel current-carrying conductors: $\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}$ (definition of Ampere).
Explain Torque on a magnetic dipole (current loop): $\vec{\tau} = \vec{M} \times \vec{B}$ ($M = NIA$) and working of Moving Coil Galvanometer.
अध्याय रूपरेखा एवं प्रगति
11. Lorentz Force & Helical Motion
22. Biot-Savart Law & Ampere's Law
33. Parallel Wires & Galvanometer
सम्पूर्ण सैद्धांतिक एवं वैचारिक अध्ययन
1. Lorentz Force & Helical Motion
A charge $q$ moving with velocity $\vec{v}$ in electric $\vec{E}$ and magnetic $\vec{B}$ fields experiences: $$\mathbf{\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})}$$ Magnetic force $\vec{F}_m = q(\vec{v} \times \vec{B})$ is always perpendicular to velocity, performing zero work ($W = 0$) and changing only direction! If $\vec{v}$ is at angle $\theta$ to $\vec{B}$, the particle executes a helical path with radius $r = \frac{mv\sin\theta}{qB}$ and pitch $p = v\cos\theta \cdot T$.
2. Biot-Savart Law & Ampere's Law
Biot-Savart Law: Magnetic field due to current element: $$\mathbf{d\vec{B} = \frac{\mu_0}{4\pi} \frac{I(d\vec{l} \times \hat{r})}{r^2}} \quad \left(\frac{\mu_0}{4\pi} = 10^{-7}\text{ T}\cdot\text{m/A}\right)$$ Field at center of circular coil: $\mathbf{B = \frac{\mu_0 N I}{2R}}$.
Ampere's Circuital Law: $\mathbf{\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}}$. Inside a long solenoid with $n$ turns per unit length: $\mathbf{B = \mu_0 n I}$.
3. Parallel Wires & Galvanometer
Parallel Currents: Attract if currents in same direction; repel if opposite. $$\mathbf{\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}} \quad (\text{SI Definition of 1 Ampere: } 2 \times 10^{-7}\text{ N/m})$$
Moving Coil Galvanometer: Deflection $\theta \propto I$ ($I = \frac{k}{NAB}\theta$). Converted to Voltmeter by adding high series resistance $R$; to Ammeter by connecting low parallel shunt resistance $S$.
Keep an error log and revisit questions that exposed a misconception.
अवधारणात्मक हल उदाहरण एवं अनुप्रयोग (Solved Examples)
उदाहरण 1
State Biot-Savart Law and write its vector form.
विस्तृत समाधान / उत्तर:
The magnetic field $d\vec{B}$ due to an infinitesimal current element $I d\vec{l}$ at distance $r$ is directly proportional to current $I$, element length $dl$, sine of angle $\theta$, and inversely proportional to $r^2$: $d\vec{B} = \frac{\mu_0}{4\pi} \frac{I (d\vec{l} \times \hat{r})}{r^2} = \frac{\mu_0}{4\pi} \frac{I (d\vec{l} \times \vec{r})}{r^3}$.
उदाहरण 2
Two parallel long straight wires carry currents of $4\text{ A}$ and $10\text{ A}$ in the same direction, separated by $10\text{ cm}$. Calculate the force per unit length between them. Is it attractive or repulsive?
विस्तृत समाधान / उत्तर:
$\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d} = \frac{(4\pi \times 10^{-7})(4)(10)}{2\pi(0.1)} = \frac{2 \times 10^{-7} \times 40}{0.1} = 8 \times 10^{-5}\text{ N/m}$. Since currents flow in the same direction, the force is attractive.
उदाहरण 3
How can a moving coil galvanometer of resistance $G$ be converted into: (i) an Ammeter of range $I$, (ii) a Voltmeter of range $V$?
विस्तृत समाधान / उत्तर:
(i) By connecting a small resistance (shunt $S = \frac{I_g G}{I - I_g}$) in parallel with the galvanometer. (ii) By connecting a large resistance ($R = \frac{V}{I_g} - G$) in series with the galvanometer.
सामान्य गलतियाँ एवं परीक्षक के जाल (Examiner Traps)
सामान्य भ्रम / गलत उत्तर
Reciting a definition without applying it to the question or data.
सही वैज्ञानिक तथ्य
Identify the concept, show the relevant evidence or calculation, and explain the final implication.
सामान्य भ्रम / गलत उत्तर
Skipping conditions, units, domain restrictions, or adjustment effects.
सही वैज्ञानिक तथ्य
State assumptions, preserve units, check boundary cases, and verify the answer against the original problem.
सामान्य भ्रम / गलत उत्तर
Treating a correct intermediate result as proof that the whole solution is correct.
सही वैज्ञानिक तथ्य
Perform an independent reasonableness check and connect the result back to the chapter principle.
Moving Charges and Magnetism - Key Conceptual & Analytical Model
अध्याय का सार संक्षेप एवं 10 मुख्य निष्कर्ष
मुख्य बिंदु 1
Lorentz Force: $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$ changing particle direction with zero work.
मुख्य बिंदु 2
Biot-Savart Law: Differential magnetic field element scaling with $I dl \sin\theta / r^2$.
मुख्य बिंदु 3
Solenoid Field: Uniform internal magnetic flux density $B = \mu_0 n I$.
मुख्य बिंदु 4
Definition of Ampere: Force of $2 \times 10^{-7}\text{ N/m}$ between parallel conductors separated by 1 meter.
मुख्य बिंदु 5
Galvanometer Conversion: High series resistance for Voltmeter; low parallel shunt for Ammeter.
स्व-मूल्यांकन अभ्यास (Check Your Understanding)
मूल वैचारिक स्पष्टता की जांच के लिए नैदानिक प्रश्न। पहले स्वयं हल करें, फिर उत्तर देखें।
1
State Biot-Savart Law and write its vector form.
उत्तर एवं व्याख्या देखें
उत्तर: The magnetic field $d\vec{B}$ due to an infinitesimal current element $I d\vec{l}$ at distance $r$ is directly proportional to current $I$, element length $dl$, sine of angle $\theta$, and inversely proportional to $r^2$: $d\vec{B} = \frac{\mu_0}{4\pi} \frac{I (d\vec{l} \times \hat{r})}{r^2} = \frac{\mu_0}{4\pi} \frac{I (d\vec{l} \times \vec{r})}{r^3}$. dB = (μ0 / 4π) (I dl × r̂) / r².
2
Two parallel long straight wires carry currents of $4\text{ A}$ and $10\text{ A}$ in the same direction, separated by $10\text{ cm}$. Calculate the force per unit length between them. Is it attractive or repulsive?
उत्तर एवं व्याख्या देखें
उत्तर: $\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d} = \frac{(4\pi \times 10^{-7})(4)(10)}{2\pi(0.1)} = \frac{2 \times 10^{-7} \times 40}{0.1} = 8 \times 10^{-5}\text{ N/m}$. Since currents flow in the same direction, the force is attractive. 8 × 10^-5 N/m (attractive).
3
How can a moving coil galvanometer of resistance $G$ be converted into: (i) an Ammeter of range $I$, (ii) a Voltmeter of range $V$?
उत्तर एवं व्याख्या देखें
उत्तर: (i) By connecting a small resistance (shunt $S = \frac{I_g G}{I - I_g}$) in parallel with the galvanometer. (ii) By connecting a large resistance ($R = \frac{V}{I_g} - G$) in series with the galvanometer. (i) Low shunt in parallel, (ii) High resistance in series.
4
Why does a charged particle moving through a uniform magnetic field experience no change in its kinetic energy?
उत्तर एवं व्याख्या देखें
उत्तर: Because the magnetic force $\vec{F}_m = q(\vec{v} \times \vec{B})$ is always perpendicular to the velocity vector $\vec{v}$ of the particle. The instantaneous power $P = \vec{F} \cdot \vec{v} = 0$, so work done is zero ($W = 0$). By the work-energy theorem, kinetic energy remains constant. Magnetic force is perpendicular to velocity, doing zero work.
5
What is the radius of the circular path of an electron of mass $m$ and charge $e$ moving with speed $v$ perpendicular to a uniform magnetic field $B$?
उत्तर एवं व्याख्या देखें
उत्तर: Magnetic Lorentz force supplies centripetal force: $\frac{m v^2}{r} = e v B \implies r = \frac{m v}{e B}$. r = mv / (eB).
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