The magnetic field at the origin due to a current element i d l → placed at a point with vector position r → is

μ 0 i 4 π r → × d l → r 3

μ 0 i 4 π d l → × r → r 2

μ 0 i 4 π r → × d l → r 2

- μ 0 i 4 π d l → × r → r 4

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The direction of induced magnetic field dB due to current element $i$ dL, at a point of distance $r$ from it, when a current $i$ passes through a long conductor is in the direction

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Important Questions on Moving Charges and Magnetism

EASY

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

The magnetic field at a point due to a current-element is directly proportional to

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

One of the two identical conducting wires of length

L

is bent in the form of a circular loop and the other one into a circular coil of

N

identical turns. If the same current is passed in both, the ratio of the magnetic field at the centre of the loop

(B_{L})

to that at the centre of the coil

(B_{C}),

i.e.

\frac{B_{L}}{B_{C}}

will be

EASY

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

Two thin metallic wires lie on $X$ and $Y$ -axes and both carry the same current as shown in the figure below. $A B$ and $C D$ are the two lines making angles $45 °$ with the axes and the origin of axes is $O$ . The magnetic field will be zero

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MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

The magnitude of the magnetic field at the centre of an equilateral triangular loop of side

1 m

which is carrying a current of

10 A

is:
[Take

μ_{0} = 4 π \times 10^{- 7} N A^{- 2}

]

EASY

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

The magnetic field at the origin due to a current element

i

d \vec{l}

placed at a point with vector position

\vec{r}

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

A point charge

Q = 3 \times 10^{- 12} C

rotates uniformly in a vertical circle of radius

R = 1 mm

. The axis of the circle is aligned along the magnetic axis of the earth. At what value of the angular speed

ω

, the effective magnetic field at the center of the circle will be reduced to zero? (Horizontal component of earth's magnetic field is

30 μ T

)

EASY

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

The C.G.S. unit of magnetic field at a point, due to Biot-Savart law is

EASY

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

An electron revolves in a circular orbit of radius

r

with angular speed

ω

. The magnetic field at the centre of electron orbit is

HARD

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

A non-conducting thin disc of radius

R

rotates about its axis with an angular velocity

w

. The surface charge density on the disc varies with the distance

r

from the center as

σ (r) = σ_{0} [1 + {(\frac{r}{R})}^{β}]

, where

σ_{0}

and

β

are constants. If the magnetic induction at the center is

B = (\frac{9}{10}) μ_{0} σ_{0} w R

, the value of

β

EASY

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

The correct Biot-Savart's law in vector form is

EASY

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

A circular coil of wire consisting of

100

turns each of radius

9 cm

carries a current of

0.4 A

. The magnitude of the magnetic field at the centre of coil is

(μ_{0} = 12.56 \times 10^{- 7} SI Units)

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

A cylindrical conductor of radius

R

is carrying a constant current. The plot of the magnitude of the magnetic field

B

with the distance

d

from the centre of the conductor is correctly represented by the figure.

HARD

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

A very long wire ABDMNDC is shown in figure carrying current I. AB and BC parts are straight, long and at right angle. At D wire forms a circular turn DMND of radius R. AB, BC parts are tangential to circular turn at N and D. Magnetic filed at the center of circle is:
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MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

A wire bent in the shape of a regular

n

polygonal loop carries a steady current

I

. Let

l

be the perpendicular distance of a given segment and

R

be the distance of a vertex both from the centre of the loop. The magnitude of the magnetic field at the centre of the loop is given by,

EASY

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

A charged particle going around in a circle can be considered to be a current loop. A particle of a mass

m

carrying charge

q

is moving in a plane with speed

v

under the influence of magnetic field

\vec{B}

. The magnetic moment of this moving particle is :

EASY

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

A square loop is made from a uniform wire as shown in the figure. If a battery is connected between the points $A & C,$ then the magnitude of the magnetic field at the center of the square is

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HARD

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field due to a Current Element, Biot-Savart Law

The current in flowing along the path $A B C D$ of a cube (shown in the left figure) produces a magnetic field at the centre of cube of magnitude $B$ . Dashed line depicts the non-conducting part of the cube.

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Consider a cubical shape shown to the right which is identical in size and shape to the left. If the same current now flows in along the path $D A E F G C D$ , then the magnitude of magnetic field at the centre will be