Obtain an expression for the magnetic induction at a point due to an infinitely long straight conductor carrying current.

Magnetic induction due to infinitely long straight conductor carrying current: XY, is an infinitely long straight conductor carrying a current I(Figure). P is a point at a distance a from the conductor. AB is a small element of length dl. θ is the angle between the current element Idl And the line joining the element dl and the point P. According to Biot-Savart law, the magnetic induction at the point P due to the current element Idl Is. dB = μ o 4 π Idl r 2 ⋅ sinθ . . . . . . ( 1 ) AC is drawn perpendicular to BP from A. ∠ OPA = ϕ , ∠ APB = dϕ In ΔABC , sinθ = ABAC = dlAC ∴ AC = dlsinθ . . . . . . . . . . ( 2 ) From ΔAPC , AC = rdϕ . . . . . . . . . ( 3 ) From equations (2) and (3), rdϕ = dlsinθ . . . . . . . . . . . . ( 4 ) Substituting equation (4) in equation (1) dB = μ o 4 π Irdϕ r 2 = μ o 4 π Idϕ r . . . . . . . . . . . . . ( 5 ) In ΔOPA , cosϕ = a r ∴ r = a cosϕ . . . . . . . . . . ( 6 ) Substituting equation (6) in equation (5) dB = μ ο 4 π 1 a cosϕdϕ The total magnetic induction at P due to the conductor XY is B = ∫ − ϕ 1 ϕ 2 dB = ∫ − ϕ 1 ϕ 2 μ o 4 πa I cosϕdϕ B = μ o 4 πa I [ sinϕ 1 + sinϕ 2 ] For infinitely long conductor, ϕ 1 = ϕ 2 = 90 o ∴ B = μ o I 2 πa If the conductor is places in a medium of permeability μ 0 , B = μ o I 2 πa

E M B I B E

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 9

MEDIUM

12th Tamil Nadu Board

IMPORTANT

Earn 100

What is permittivity and permeability of free space? Establish the relation between them.

Important Questions on Magnetism And Magnetic Effects of Electric Current

EASY

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 10

Find the percent increase in the magnetic field

B

when the space within a current-carrying toroid is filled with aluminum. The susceptibility of aluminum is

2 \times 10^{- 5}

.

EASY

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 11

The magnetic susceptibility is negative and very small for -

EASY

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 12

The cause of diamagnetism is-

EASY

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 13

Magnetic moment of diamagnetic substances-

EASY

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 14

A domain in ferromagnetic iron is in the form of a cube of side length

2

μm

, then the number of iron atoms in the domain are: (Molecular mass of iron is

55 g m o l^{- 1}

and density is

7.92 g c m^{- 3}

)

EASY

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 15

Answer the following question.

Is the permeability of a ferromagnetic material independent of the magnetic field? If not, is it more for lower or higher fields?

EASY

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 16

Answer the following question:

Magnetic field lines are always nearly normal to the surface of a ferromagnet at every point. (This fact is analogous to the static electric field lines being normal to the surface of a conductor at every point.) Why?

EASY

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 17

What is the behaviour of diamagnetic, paramagnetic and ferromagnetic substance in non-uniform magnetic field?