Obtain an expression for the magnetic flux density B ⇀ at the centre of a circular coil of radius R having N turns when a current I flows through it.

* Magnetic field due to circular coil carrying current : consider a small current element of dl on a ring. Let R be the distance from this dl to centre O of the ring then According to Biot-Savart law, dB = μ 0 4 π I dl sin θ R 2 Here θ = Angle between dl → & R → = 90 ° ⇒ dB = μ 0 4 π I dl R 2 Now magnetic field at the centre of circular coil carrying current = B = ∫ 0 2 π R μ 0 Idl 4 π R 2 = μ 0 I 4 π r 2 ∫ 0 2 π R dl= μ 0 I 4 π R 2 × 2 π R ⇒ B= μ 0 I 2 R For N turns in the coil magnetic field is expressed as B= μ 0 NI 2 R

Give the defining vector equation of magnetic field B ⇀ in terms of the force F ⇀ acting on a charge q moving in the field with a velocity v ⇀ . Using this equation, express the SI unit of B ⇀ in terms of the fundamental (base) SI units.

Force on a charge due to magnetic field B → F = q v → ∝ B → F = q v B sin θ ∴ B = F v sin θ 1 Tesla: Magnitude of field is 1 T when 1 C charge moves with velocity 1 m / s perpenduculer to the uniform field experiences a force of 1 N . S.I unit of B = NS / c / m = N / A / m .

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12th ICSE

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A current is flowing through a thin, straight metallic conductor of infinite length. Find expression for the magnetic field at a distance from it.

Important Questions on Moving Charges and Magnetic Field

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12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 7 - Moving Charges and Magnetic Field>QUESTIONS>Q 4

Write an expression for Biot-Savart’s law in vector form. Derive an expression for magnetic field at the centre of a circular current-carrying coil of radius r, with N turns.

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12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 7 - Moving Charges and Magnetic Field>QUESTIONS>Q 5

Obtain an expression for the magnetic flux density

\overset{⇀}{B}

at the centre of a circular coil of radius

R

having

N

turns when

a

current

I

flows through it.

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12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 7 - Moving Charges and Magnetic Field>QUESTIONS>Q 6

State Ampere’s circuital law connecting the line integral of

\overset{⇀}{B}

over a closed path to the net current crossing the area bounded by the path.
Use the law to derive expression for magnetic field due to an infinitely-long straight current-carrying wire. Why is the above derivation not valid for magnetic field due to a current-carrying wire of finite length?

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12th ICSE

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NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 7 - Moving Charges and Magnetic Field>QUESTIONS>Q 7

State Ampere’s circuital law. Use it to obtain magnetic field due to a long, straight solenoid.

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12th ICSE

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NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 7 - Moving Charges and Magnetic Field>QUESTIONS>Q 8

Using Ampere’s circuital law, obtain an expression for the magnetic flux density ‘B’ at a point X at a perpendicular distance r from a long current-carrying conductor.

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12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 7 - Moving Charges and Magnetic Field>QUESTIONS>Q 9

Give the defining vector equation of magnetic field

\overset{⇀}{B}

in terms of the force

\overset{⇀}{F}

acting on a charge

q

moving in the field with a velocity

\overset{⇀}{v}

. Using this equation, express the SI unit of

\overset{⇀}{B}

in terms of the fundamental (base) SI units.

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12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 7 - Moving Charges and Magnetic Field>QUESTIONS>Q 10

Derive an expression for the magnetic field inside a toroid. Explain how it is different from the result obtained in case of a tightly wound long-solenoid.

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12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 7 - Moving Charges and Magnetic Field>QUESTIONS>Q 11

Describe the motion of a charged particle in a uniform magnetic field. Show that for a charged particle moving perpendicular to a magnetic field, the radius of the path is proportional to the momentum

(mu)

and inversely proportional to the specific charge

(e / m)

of the particle. Also prove that the frequency of revolution of the particle is independent of its speed.

A current is flowing through a thin, straight metallic conductor of infinite length. Find expression for the magnetic field at a distance from it.

Important Questions on Moving Charges and Magnetic Field

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