6 public questions tagged with this topic.
**Sign of potential energy** indicates nature of interaction, like charges U>0, opposite U
Ref: NCERT > Physics Book > Electrostatic Potential and Capacitance > Potential Energy of System of Charges
**Permanent magnet requirement** is high retentivity to maintain field and high coercivity to resist demagnetization. Ability to retain magnetism after field removal is property of hard ferromagnets, related to domain wall pinning and anisotropy. U_m = -m B cosθ . Given: m = 0.8 A m² , B = 0.3 T , θ = 90° , cos 90° = 0 . U_m = -0.8 × 0.3 × 0 = 0 J . Substituting values gives 0 J, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.
Ref: NCERT > Physics Book > Magnetism and Matter > Hysteresis, Retentivity, Coercivity and Permanent Magnets
**Magnetic properties** μ_r = 400 indicates 400 times vacuum permeability, so B enhanced 400 times for same nI. H = nI (A/m) for solenoid, M = χ H, B = μ₀(H+M) links microscopic magnetization to macroscopic field. U_m = -m B cosθ . Given: m = 0.9 A m² , B = 0.2 T , θ = 90° , cos 90° = 0 . Substitute: U_m = -0.9 × 0.2 × 0 = 0 J . Substituting values gives 0 J, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.
Ref: NCERT > Physics Book > Magnetism and Matter > Magnetization, Magnetic Intensity, Susceptibility and Permeability
**Magnetic dipole in uniform field** experiences torque τ = m B sinθ and potential energy U = -m·B = -m B cosθ, minimum -mB when aligned (θ=0°), maximum +mB at anti-alignment (θ=180°). Work done rotating from θ₁ to θ₂ equals ΔU = mB(cosθ₁ - cosθ₂). U_m = -m B cosθ . Given: m = 0.3 A m² , B = 0.4 T , θ = 90° , cos 90° = 0 . U_m = -0.3 × 0.4 × 0 = 0 J . Substituting values gives 0 J, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.
Ref: NCERT > Physics Book > Magnetism and Matter > Torque on Magnetic Dipole and Potential Energy
**Torque on magnetic dipole** in uniform field B is τ = m × B, magnitude τ = m B sinθ, m moment (A·m²), B field (T), θ angle between m and B (degrees). Torque tends to align moment with field, zero at θ = 0°, maximum mB at 90°, direction given by right-hand rule. The torque on a magnetic dipole is given by tau = m B sinθ . It reaches its maximum value when sinθ = 1 , which occurs at θ = 90° (perpendicular orientation), as the cross product m × B is greatest when the angle between the dipole moment and field
Ref: NCERT > Physics Book > Magnetism and Matter > Torque on Magnetic Dipole and Potential Energy
**Dipole moment** governs torque and energy in external field. Axial field stronger than equatorial, torque maximum at θ = 90°, zero when aligned. Work done rotating dipole relates to ΔU = pE(1 - cosθ), explaining stable equilibrium at θ = 0°. Dipole moment: p = q × 2a = 2 × 10⁻⁶ × 1 × 10⁻³ = 2 × 10⁻⁹ C m . Torque: tau = p E sin θ = 2 × 10⁻⁹ × 6 × 10⁴ × sin 90° = 1.2 × 10⁻⁴ N m . Substituting values gives 1.2 × 10⁻⁴ N m, which matches expected magnitude for this electrostatic configuration, confirming
Ref: NCERT > Physics Book > Electric Charges and Fields > Electric Dipole - Moment, Field and Torque
