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2. De Broglie wavelength λ associated with a particle having a momentum p is given by :
λ = h / p. h = Planck's constant.
p = m v , where v = speed, and m = mass of the particle.
E = Kinetic Energy of the particle = 1/2 m v² = p² / 2m
p = √[2 m E]
So λ = h / [√ 2 m E ]
When a charge particle of charge q is accelerated through a potential difference of V, the kinetic energy gained by the particle = the work done on the particle by electrostatic force.
E = W = V * q.
λ = h / √[ 2mqV ]
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1. Mutual Inductance between two coils :
i₁ & i₂ are currents in the two coils. B₁ & B₂ are magnetic fields due to coils 1 and 2. Φ_B₁ and Φ_B₂ are the magnetic fluxes passing through the coils 1 and 2. N₁ and N₂ are the number of turns in the coils. A₁ and A₂ are areas of the coils.
M₁₂ = N₁ N₂ * (μ A / L)
M₁₂ = (N₂ * Φ_B₂) / i₁ = M₂₁ = (N₁ * Φ_B₁) / i₂
N₂ * Φ_B₂ is the magnetic flux caused by the Coil 1 on the coil 2, due to its current i₁.
Magnetic flux Φ_B₂ is proportional to the magnetic field B₁ and the number of turns N₁ due to i₁. Also It is proportional inversely to cube of the distance between the coils.
Φ_B₂ = B₁ * A₂ , A₂ = area of the coil 2.
B₁ due to a coil 1 = (μ/4π) * 2 (N₁ i₁ A₁) / d³,
Coils are separated by distance d, d >> R , R = radii of the coils.
Clearly the Mutual Induction is proportional to the number of turns in both coils. Also it is inversely proportional to the cube of distance between them.
If the number of turns increases, the mutual inductance increases.
If the distance increases, the Mutual Inductance decreases.
λ = h / p. h = Planck's constant.
p = m v , where v = speed, and m = mass of the particle.
E = Kinetic Energy of the particle = 1/2 m v² = p² / 2m
p = √[2 m E]
So λ = h / [√ 2 m E ]
When a charge particle of charge q is accelerated through a potential difference of V, the kinetic energy gained by the particle = the work done on the particle by electrostatic force.
E = W = V * q.
λ = h / √[ 2mqV ]
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1. Mutual Inductance between two coils :
i₁ & i₂ are currents in the two coils. B₁ & B₂ are magnetic fields due to coils 1 and 2. Φ_B₁ and Φ_B₂ are the magnetic fluxes passing through the coils 1 and 2. N₁ and N₂ are the number of turns in the coils. A₁ and A₂ are areas of the coils.
M₁₂ = N₁ N₂ * (μ A / L)
M₁₂ = (N₂ * Φ_B₂) / i₁ = M₂₁ = (N₁ * Φ_B₁) / i₂
N₂ * Φ_B₂ is the magnetic flux caused by the Coil 1 on the coil 2, due to its current i₁.
Magnetic flux Φ_B₂ is proportional to the magnetic field B₁ and the number of turns N₁ due to i₁. Also It is proportional inversely to cube of the distance between the coils.
Φ_B₂ = B₁ * A₂ , A₂ = area of the coil 2.
B₁ due to a coil 1 = (μ/4π) * 2 (N₁ i₁ A₁) / d³,
Coils are separated by distance d, d >> R , R = radii of the coils.
Clearly the Mutual Induction is proportional to the number of turns in both coils. Also it is inversely proportional to the cube of distance between them.
If the number of turns increases, the mutual inductance increases.
If the distance increases, the Mutual Inductance decreases.
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