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

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Diagram shows a bar magnet and two infinite long wires $W_{1}$ and $W_{2}$ carrying equal currents in opposite directions. The magnet is free to move and rotate. $P$ is the mid-point of magnet. For this situation mark out the correct statement(s)

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Important Questions on Magnetism And Magnetic Effects of Electric Current

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 88

Statement-1: A copper disk is secured on a horizontal axis and placed between the poles of a strong magnet so that the north pole of the magnet is arranged on the right. The bottom of the disk is immersed in a cup of mercury. When the axis of the disk and the mercury cup are connected to a d-c source then ring starts rotating.

Statement-2: Due to the current which flows through the disk, net torque acts on the disk.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 89

A circular coil of

30

turns and radius

8.0 cm

carrying a current of

6.0 A

is suspended vertically in a uniform horizontal magnetic field of magnitude

1.0 T

. The field lines make an angle of

60 °

with the normal of the coil. A counter torque is applied to prevent the coil from turning. Would your answer change, if the circular coil were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered.)

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12th Tamil Nadu Board

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 90

A rectangular current loop $EFGH$ is placed in uniform magnetic field, as shown in the figure. What will be the direction of torque on loop?

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 91

A square coil of side

10 cm

consists of

20 turns

and carries a current of

12 A

. The coil is suspended vertically, and the normal to the plane of the coil makes an angle of

30 °

with the direction of a uniform horizontal magnetic field of magnitude

0.80 T

. What is the magnitude of torque experienced by the coil.

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12th Tamil Nadu Board

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 92

A square coil of side

10 cm

and

20

turns have a current

12 A

is suspended vertically. If its area vector makes an angle

30 °

with uniform magnetic field of

0.08 T

. Find the torque on the coil.

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12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 93

With the help of neat diagram, describe construction, theory and working of a moving coil galvanometer.

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12th Tamil Nadu Board

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 94

State Coulomb’s inverse law for magnetism.

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12th Tamil Nadu Board

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Magnetism And Magnetic Effects of Electric Current>Exercise>Q 95

Explain electrostatic analogue of magnetic dipole

Diagram shows a bar magnet and two infinite long wires W1 and W2 carrying equal currents in opposite directions. The magnet is free to move and rotate. P is the mid-point of magnet. For this situation mark out the correct statement(s)

Important Questions on Magnetism And Magnetic Effects of Electric Current

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Diagram shows a bar magnet and two infinite long wires $W_{1}$ and $W_{2}$ carrying equal currents in opposite directions. The magnet is free to move and rotate. $P$ is the mid-point of magnet. For this situation mark out the correct statement(s)