Two infinitely long straight wires lie in the xy - plane along the lines x = ± R . The wire located at x = + R carries a constant current I 1 and the wire located at x = - R carries a constant current I 2 . A circular loop of radius R is suspended with its centre at 0 , 0 3 R and in a plane parallel to the xy - plane. This loop carries a constant current I in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the + j ^ direction. Which of the following statements regarding the magnetic field B → is (are) true?

If I 1 = I 2 , Then the z - component of the magnetic field at the centre of the loop is - μ 0 I 2 R

If I 1 < 0 a n d I 2 > 0 , t h e n B → can be equal to zero at the origin 0 , 0 , 0

EASY

Earn 100

Derive the expression for magnetic field at a point on the axis of a circular current carrying loop.

Important Questions on Magnetic Effect of Electric Current

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

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

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HARD

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

Two identical wires

A

and

x -

, 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}}

HARD

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

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:

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

What is the magnetic field at the centre of arc in the figure below?

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MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of

10 A .

The magnetic field at point

O

will be close to:
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EASY

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

A current

i

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

O

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

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}) .

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

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>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

An electron moving in a circular orbit of radius

r

makes

n

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

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

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

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

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

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MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

A circular coil carrying current

I

has a radius

R

and magnetic field at the centre is

B

. The distance from the centre along the axis of the same coil where the magnetic field will be

\frac{B}{8}

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

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.

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

A wire $A$ , bent in the shape of an arc of a circle, carrying a current of $2 A$ and having radius $2 cm$ and another wire $B$ , also bent in the shape of an arc of a circle, carrying a current of $3 A$ and having radius of $4 cm$ , are placed as shown in the figure. The ratio of the magnetic fields due to the wires $A$ and $B$ at the common centre $O$ is:

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EASY

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

Figure below shows three circuits consisting of concentric circular arcs and straight radial lines. The center of the circle is shown by the dot. Same current flows through each of the circuits. If $B_{1}, B_{2}, B_{3}$ are the magnitudes of the magnetic field at the center. Which of the following is true?

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EASY

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

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

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

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

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

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>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

Two infinitely long straight wires lie in the xy - plane along the lines

x = \pm R

. The wire located at

x = + R

carries a constant current

I_{1}

and the wire located at

x = - R

carries a constant current

I_{2}

. A circular loop of radius R is suspended with its centre at

(0, 0 \sqrt{3} R)

and in a plane parallel to the xy - plane. This loop carries a constant current

I

in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the

+ \hat{j}

direction. Which of the following statements regarding the magnetic field

\vec{B}

is (are) true?

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Electric Current>Magnetic Field Due to a Current Carrying Circular Loop

A Helmholtz coil has a pair of loops, each with

N

turns and radius

R

. They are placed coaxially at distance

R

and the same current

I

flows through the loops in the same direction. The magnitude of the magnetic field at

P,

midway between the centres

A

and

C,

is given by [Refer to figure given below]:
Question Image

Derive the expression for magnetic field at a point on the axis of a circular current carrying loop.

Important Questions on Magnetic Effect of Electric Current

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