The magnetic moment of two bar magnets are M 1 → and M 2 → . If angle between them is θ , then write the value of resultant magnetic moment.

Given, Magnetic moment of two bar magnet is M 1 a n d M 2 Angle between them is θ Therefore, Resultant magnetic moment= M 1 2 + M 2 2 + 2 M 1 M 2 C o s θ This is our required answer.

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A short bar magnet has a magnetic moment of $0.65 J T^{- 1}$ then the magnitude and direction of the magnetic field produced by the magnet at a distance $8 cm$ from the centre of magnet on the axis is

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Important Questions on Magnetic Effects of Electric Current

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An insulating thin rod of length

l

has a linear charge density

ρ (x) = ρ_{0} \frac{x}{l}

on it. The rod is rotated about an axis passing through the origin

(x = 0)

and perpendicular to the rod. If the rod makes

n

rotations per second, then the time averaged magnetic moment of the rod is:

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A thin rod of length

L

is magnetized and has magnetic moment

M

. The rod is then bent in a semicircular arc. The magnetic moment in the new shape is

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A large magnet is broken into two pieces so that their lengths are in the ratio

1 : 2

. The ratio of their magnetic moments is

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What is magnetic dipole moment? Derive the expression for torque on a bar magnet placed in a uniform magnetic field.

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A circular coil having

N

turns and radius

r

carries a current

I .

It is held in the

X Z

plane in a magnetic field

B \hat{i}

. The torque on the coil due to the magnetic field is:

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The magnetic moment of two bar magnets are

\vec{M_{1}}

and

\vec{M_{2}}

. If angle between them is

θ

, then write the value of resultant magnetic moment.

HARD

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A bar magnet of length

14 cm

is placed in the magnetic meridian with its north pole pointing towards the geographic north pole. A neutral point is obtained at a distance of

18 cm

from the center of the magnet. If

B_{H} = 0.4 G

, the magnetic moment of the magnet is

(1 G = 10^{- 4} T)

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What is the magnitude of the equatorial fields due to a bar magnet of length

5.0 cm

at a distance

75 cm

from its mid point? The magnetic moment of the bar magnet is

0.75 A m^{2}

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A square loop is carrying a steady current

I

and the magnitude of its magnetic dipole moment is

m

. If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be:

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Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole

\vec{m} .

Which configuration has highest net magnetic dipole moment?

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Write SI unit of magnetic dipole moment..

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Two short bar magnets of length

1 cm

each have magnetic moments

1 .20 A m^{2}

and

1 .00 A m^{2}

respectively. They are placed on a horizontal table parallel to each other with their

N

poles pointing towards the south. They have a common magnetic equator and are separated by a distance of

20 .0 cm

. The value of the resultant horizontal magnetic induction at the mid-point

O

of the line joining their centres is close to
( Horizontal component of earth's magnetic induction is

3 .6 \times 10^{- 5} Wb m^{- 2}

)

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A straight steel wire of length

l

has magnetic moment

m

. If the wire is bent in the form of a semicircle, what is the new value of the magnetic dipole moment?

MEDIUM

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A long magnetic needle of length

2 l

magnetic moment

M

and pole strength

m

is broken into two pieces at the middle. The magnetic moment and pole strength of each piece will be

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A bar magnet of magnetic moment

M

is bent to form a semicircle. What is the magnetic moment of the bent magnet?

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A magnetic needle of magnetic moment

6 .7 \times 10^{- 2} A m^{2}

and moment of inertia

7 .5 \times 10^{- 6} kg m^{2}

is performing simple harmonic oscillations in a magnetic field of

0.01 T

. Time taken for

10

complete oscillations is:

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A short bar magnet is placed in the magnetic meridian of the earth with North Pole pointing north. Neutral points are found at a distance of $30 cm$ from the magnet on the East-West line, drawn through the middle point of the magnet. The magnetic moment of the magnet in ${Am}^{2}$ is close to:

(Given $\frac{μ_{0}}{4 π} = 10^{- 7}$ in SI units and $B_{H} =$ Horizontal component of earth's magnetic field $= 3.6 \times 10^{- 5}$ Tesla.)

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The magnetic dipole moment of a short magnetic dipole at a distant point along the equator of magnet has a magnitude of

X

in SI units. If the distance between point and the magnet is halved then the magnitude of dipole moment will be

HARD

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The magnetic flux near the axis and inside the air-core solenoid of length

60 cm

carrying current

I

1.57 \times 10^{6} Wb .

Its magnetic moment will be (cross-sectional area of a solenoid is very small as compared to its length,

μ_{0} = 4 π \times 10^{- 7}

SI units)

HARD

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A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are

T_{h}

and

T_{c}

respectively, then:

A short bar magnet has a magnetic moment of 0.65 J T-1 then the magnitude and direction of the magnetic field produced by the magnet at a distance 8 cm from the centre of magnet on the axis is

Important Questions on Magnetic Effects of Electric Current

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A short bar magnet has a magnetic moment of $0.65 J T^{- 1}$ then the magnitude and direction of the magnetic field produced by the magnet at a distance $8 cm$ from the centre of magnet on the axis is