#external field

Solenoid, Toroid and Ampere's Law

Why is the magnetic field outside a long solenoid considered negligible?

**Solenoid field** inside long solenoid is B = μ₀ n I, n = N/L turns per meter (m⁻¹), uniform and parallel to axis, outside negligible for long solenoid because fields from opposite sides cancel. For n = 1200 m⁻¹, I = 1 A, B = 4π×10⁻⁷×1200 = 1.51×10⁻³ T = 1.51 mT. In a long solenoid, the magnetic field lines are concentrated inside, and outside, the fields from opposite sides of the coils cancel each other, making the external field nearly zero. Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r), B = μ₀ N I/(2R)

Ref: NCERT > Physics Book > Moving Charge and Magnetism > Solenoid, Toroid and Ampere's Law

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Solenoid with Magnetic Core and Magnetic Properties

The primary reason a diamagnetic material develops a weak opposing magnetic moment in an external field is:

**Solenoid with magnetic core** produces field B = μ₀ μ_r n I inside, μ₀ = 4π×10⁻⁷ T·m/A, μ_r relative permeability, n = N/L turns per meter, I current. Core enhances field μ_r times, so given B, μ_r, n, current I = B/(μ₀ μ_r n) can be found, illustrating core effect on field strength. In diamagnetic materials, an external magnetic field induces orbital currents in atoms that oppose the applied field, per Lenz’s law. This results in a weak, negative magnetization, as all electrons contribute to this effect in materials with no net magnetic moment. Substituting values gives Induced currents opp

Ref: NCERT > Physics Book > Magnetism and Matter > Solenoid with Magnetic Core and Magnetic Properties

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Electric Dipole - Moment, Field and Torque

A dipole with charges \( +6 \, \mu\text{C} \) and \( -6 \, \mu\text{C} \) separated by 4 mm is in a field \( 5 \times 10

**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 = 6 × 10⁻⁶ × 4 × 10⁻³ = 2.4 × 10⁻⁸ C m . Torque: tau = p E sin θ = 2.4 × 10⁻⁸ × 5 × 10⁴ × sin 60° = 1.2 × 10⁻³ × (√(3)/2) = 1.04 × 10⁻³ N m . Substituting values gives 1.04 × 10⁻³ N m, which matches expected

Ref: NCERT > Physics Book > Electric Charges and Fields > Electric Dipole - Moment, Field and Torque

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Superposition Principle and Equilibrium of Charges

Why is the electric field inside a conductor zero when it is placed in an external electric field?

**Superposition principle** asserts net Coulomb force on charge equals vector sum of forces from each other charge independently, F_net = Σ F_i, where F_i = k q q_i/r_i² r̂_i. In equilateral triangle or square symmetry, components may cancel at centroid, producing equilibrium. In a conductor, free charges redistribute in response to an external field until the internal field cancels the external field completely. This equilibrium condition ensures no net field exists inside, as any field would cause charge motion, violating static conditions. Substituting values gives Charge redistribution, wh

Ref: NCERT > Physics Book > Electric Charges and Fields > Superposition Principle and Equilibrium of Charges

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