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Infinite conducting ring each having current $i$ in the direction shown are placed concentrically in the plane as shown in the figure. The radius of rings are $r, 2 r, 2^{2} r, 2^{3} r \dots \dots \dots \infty$ . The magnetic field at the centre of ring will be

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Important Questions on Electrostatics

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Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

The magnetic field at the centre $O$ of the current-carrying square loop shown in the figure is

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Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

The magnetic field at the centre ${}^{'}O^{'}$ in the given figure is

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Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

A current

i

flows through a loop as shown in figure. The magnetic field at the Centre

O

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Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

Two circular loops

L_{1}

and

L_{2}

of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop

L_{1}

R_{1}

and that of

L_{2}

R_{2}

. The distance between the centres of the loops is

\sqrt{3} R_{1}

. The magnetic field at the centre of

L_{2}

shall be zero if

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Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

The magnitude of a magnetic field at the centre of a circular coil of radius

R

, having

N

turns and carrying a current

I

can be doubled by changing

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

Let

{\vec{B}}_{1}

is the magnetic field at the centre of the current carrying coil of radius

R

and

{\vec{B}}_{2}

is the magnetic field on the axis of same circular coil at the distance of

3 R .

Then the ratio

\frac{|{\vec{B}}_{1}|}{|{\vec{B}}_{2}|}

EASY

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

The magnetic field at the centre of a circular coil of

50

turns and radius

10 cm

carrying a current of

1 A,

in tesla is

HARD

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

A circular coil connected to a battery of emf

E

produced a certain magnetic induction field at its centre. The coil is unwound, stretched to double its length rewound into a coil of

\frac{1^{rd}}{3}

of the original radius and connected to a battery of emf

E^{'}

to produce same field at the centre. Then

E^{'}

HARD

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

Two identical wires

A

and

B

, each of length

l

, carry the same current

I

. Wire

A

is bent into a circle of radius

R

and wire

B

is bent to form a square of side

a

. If

B_{A}

and

B_{B}

are the values of magnetic field at the centres of the circle and square respectively, then the ratio

\frac{B_{A}}{B_{B}}

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

A thin ring of

10 c m

radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of

40 π r a d s^{- 1}

about its axis, perpendicular to its plane. Is the magnetic field its centre is

3.8 \times 10^{- 9} T

, then the charge carried by the ring is close to

(μ_{0} = 4 π \times 10^{- 7} N A^{- 2}) .

EASY

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

A circular coil of radius

R

carries an electric current

I

. The magnetic field due to the coil at a point on the axis of the coil located at a distance

r

from the centre of the coil, such that

r ≫ R,

the magnetic field at that point is proportional to

EASY

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is

B .

It is then bent into a circular coil of

n

turns. The magnetic field at the centre of this coil of

n

turns will be

EASY

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

Magnetic field at the centre of a circular loop of area

A

B

. The magnetic moment of the loop will be (

μ_{0} =

permeability of free space)

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Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

The coefficient of self-induction of a closely wound coil of

100

turns and area of cross-section

1 {cm}^{2}

1 mH

. Find the magnetic induction at the centre of its core when a current of

2 A

flows in it.

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

A circular loop of radius

r

of conducting wire connected with a voltage source of zero internal resistance produces a magnetic field

B

at its centre. If instead, a circular loop of radius

2 r

, made of same material, having the same cross-section is connected to the same voltage source, what will be the magnetic field at its centre?

EASY

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

A certain length of insulated wire can be bent to form either a single circular loop (case I) or a double loop of smaller radius (case II). When the same steady current is passed through the wire, the ratio of the magnetic field at the centre in case I to that in case II is

HARD

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

A light charged particle is revolving in a circle of radius

r

in electrostatic attraction of a static heavy particle with opposite charge. How does the magnetic field

B

at the centre of the circle due to the moving charge depend on

r

HARD

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

A small circular loop of conducting wire has radius a and carries current

I .

It is placed in a uniform magnetic field

B

perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period

T .

The mass of the loop is

m

then:

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

Two infinitely long wires each carrying current

I

along the same direction are made into the geometry as shown in the figure below.
Question Image

The magnetic field at the point

P

EASY

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

An electron moving in a circular orbit of radius

r

makes

n

rotations per second. The magnetic field produced at the center has magnitude:

Infinite conducting ring each having current i in the direction shown are placed concentrically in the plane as shown in the figure. The radius of rings are r, 2r, 22r, 23r………∞ . The magnetic field at the centre of ring will be

Important Questions on Electrostatics

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Infinite conducting ring each having current $i$ in the direction shown are placed concentrically in the plane as shown in the figure. The radius of rings are $r, 2 r, 2^{2} r, 2^{3} r \dots \dots \dots \infty$ . The magnetic field at the centre of ring will be