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Biot-savart's law - class-XI

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Which of the following entities are closely associated to each other

  1. Gravitation and nuclear fusion

  2. Electricity and magnetism

  3. Chemical Bonding and Planetary motion

  4. None


Correct Option: B
Explanation:

Electric current and magnetism are very closely related phenomenon and both can be generated using the other.

Define Electromagnetism

  1. The study of attraction or repulsion between two magnets is called electromagnetism

  2. The study of electric effects due to magnetic interaction is called electromagnetism

  3. The study of magnetic effects produced due to electric current is called electromagnetism

  4. The study of magnetic effects produced due to electric charge is called electromagnetism


Correct Option: C
Explanation:

Electromagnetism is study of various phenomenon related to electricity and magnetism. 

Which of the following phenomenon can be related to electric current 

  1. Magentism

  2. Gravitation

  3. Nuclear Fission

  4. Chemical Bonding


Correct Option: A
Explanation:

Electric current and magnetism are very closely related phenomenon and both can be generated using the other.

The Magnetic effect of current was discovered by:

  1. John Ambrose Fleming

  2. Hans Christian Oersted

  3. Michael Faraday

  4. André-Marie Ampère


Correct Option: B
Explanation:
The magnetic effect of an electric current was discovered by Hans Christian Oersted in 1820. He demonstrated the effect by plotting compass close to a long straight wire which is carrying current and noting it's deflection. And the by reversing the direction of the current, the compass needle was deflected in the opposite sense.

How can you determine direction of magnetic field lines around a current carrying conductor

  1. Left hand Thumb Rule

  2. Right Hand Thumb Rule

  3. By rotating the conductor

  4. Using sonometer


Correct Option: B
Explanation:

Direction of magnetic field lines around a current carrying conductor can be found by RIght Hand Thumb Rule.

One metal wire is kept in east-west direction.  $I$  is the current flow due west. Then, due to magnetic field  $\vec { { B } }$  of the earth on the wire is in the........ Direction.

  1. downward

  2. Upward

  3. north

  4. south


Correct Option: C
Explanation:
according to left hand rule. if current is in west direction then magnetic field will be north direction, if force is in north west direction

A moving charge produces

  1. Neither electric field nor magnetic field

  2. Electro-static field only

  3. Magnetic field only

  4. Both magnetic and electro-static field


Correct Option: D
Explanation:

A charged particle produces an electric field around it independent of its motion. But when it is at rest, it doesn't produce a magnetic field. 

When it starts moving, it additionally produces a magnetic field too.

SI unit of permittivity of free space is:

  1. Farad

  2. Weber

  3. ${ C }^{ 2 }{ N }^{ -1 }{ m }^{ -2 }$

  4. ${ C }^{ 2 }{ N }^{ -1 }{ m }^{ -1 }$


Correct Option: C
Explanation:

Coulombic force between two charges is given by

F=1/4π€ (q'.q″/r²)

From here, the SI UNIT of permittivity comes out is

= coulomb²/Newton-meter²

C²/N-m²

If an electron is moving with velocity $\bar{v}$ produces a magnetic field $\bar{B}$, then

  1. the direction of field $\bar{B}$ will be same as the direction of velocity $\bar{v}$

  2. the direction of field $\bar{B}$ will be opposite as the direction of velocity $\bar{v}$

  3. the direction of field $\bar{B}$ will be perpendicular as the direction of velocity $\bar{v}$

  4. the direction of field $\bar{B}$ does not depend upon the direction of velocity $\bar{v}$


Correct Option: C
Explanation:

According to Biot-Savart's law, the magnetic field
$\displaystyle \overset{\rightarrow}{B} = \frac{\mu _o}{4 \pi} . \frac{q (\overset{\rightarrow}{v} \times \overset{\rightarrow}{r} ) }{r^3}$
The direction of $\overset{\rightarrow}{B}$ will be along $\overset{\rightarrow}{v} \times \overset{\rightarrow}{r}$ i.e. perpendicular to the plane containing $\overset{\rightarrow}{v}$ and $\overset{\rightarrow}{r}$.

Biot-Savart law indicates that the moving electrons (velocity $\bar v$ ) produce a magnetic field $\bar B$ such that:

  1. $\bar B \perp \bar v$

  2. $\bar B \parallel \bar v$

  3. it obeys inverse cube law.

  4. it is along the line joining the electron and point of observation.


Correct Option: A
Explanation:

Magnetic field produced by charges moving with velocity $\bar v$, at a distance r is $ \bar B$ = $\left ( \dfrac{\mu _0}{4\pi } \right )$.q$\dfrac{\bar v \times \hat r}{r^2}$
Therefore $\bar B \perp \bar v$

A particle of charge per unit mass $\alpha$  is released from origin with a velocity $\mathop v\limits^ \to   = {v _0}\mathop i\limits^ \wedge  $ in a uniform magnetic field $\mathop B\limits^ \to   =  - {B _0}\mathop k\limits^ \wedge  $ . If the particle passes through (0,y,0) then y is
equal to

  1. $ - \frac{{2{v _0}}}{{{B _0}\alpha }}\,\;$

  2. $\frac{{{v _0}}}{{{B _0}\alpha }}\;$

  3. $\;\frac{{2{v _0}}}{{{B _0}\alpha }}$

  4. $ - \frac{{{v _0}}}{{{B _0}\alpha }}$


Correct Option: C

A vertical straight conductor carries a current vertically upwards. A point P lies to the east of it at a small distance and another point Q lies to the west at the same distance the magnetic field at P is :

  1. greater than at Q

  2. same as at Q

  3. less than at Q

  4. greater or less than at Q depending upon the strength of current


Correct Option: B
Explanation:

As per Biot Savart Law, Magnetic field at a point is inversely proportional to square of distance from the current carrying conductor. Therefore magnitude of magnetic field is same at both points P and Q, irrespective of their position from the conductor.

If a current carrying wire carries 10A current then the magnetic field is X. Now the current in the wire increases to 100A, them magnetic field in the wire becomes

  1. >X

  2. <X

  3. =X

  4. all


Correct Option: A
Explanation:

The Magnitude of magnetic field produced by a straight current carrying wire at a given point is
A) directly proportional to the current passing in the wire and
B) inversely proportional to the distance of that point from the wire.

The magnetic field produced by a current-carrying wire at a given point depends on

  1. the current passing through it.

  2. the voltage across it

  3. the power through it

  4. all


Correct Option: A
Explanation:

The magnetic field produced by a current-carrying wire at a given point depends directly on the current passing through it. Therefore, if there is a circular coil having n turns, the field produced is n times as large as that produced by a single turn. This is because the current in each circular turn has the same direction, and the field due to each turn then just adds up.

If magnetic field produced by a straight current carrying wire at a distance 10cm from it is X. Then the magnetic field produced at a distance 29cm will be

  1. >X

  2. <X

  3. =X

  4. all


Correct Option: B
Explanation:

The Magnitude of magnetic field produced by a straight current carrying wire at a given point is 
A) directly proportional to the current passing in the wire and 
B) inversely proportional to the distance of that point from the wire.

Which of the following relation represents Biot-Savart's law?

  1. $\vec { dB } =\dfrac { { \mu } _{ 0 } }{ 4\pi } \dfrac { \vec { dl } \times \vec { r } }{ r } $

  2. $\vec { dB } =\dfrac { { \mu } _{ 0 } }{ 4\pi } \dfrac { \vec { dl } \times \hat { r } }{ { r }^{ 3 } } $

  3. $\vec { dB } =\dfrac { { \mu } _{ 0 } }{ 4\pi } \dfrac { \vec { dl } \times \vec { r } }{ { r }^{ 3 } } $

  4. $\vec { dB } =\dfrac { { \mu } _{ 0 } }{ 4\pi } \dfrac { \vec { dl } \times \vec { r } }{ { r }^{ 4 } } $


Correct Option: C
Explanation:

If unit current is flowing through the conductor, then Biot-Savart's law is represented as
    $\vec { dB } =\dfrac { { \mu  } _{ 0 } }{ 4\pi  } \dfrac { \vec { dl } \times \vec { r }  }{ { r }^{ 3 } } $

A long cylindrical wire of radius R carries a current $i$ distributed uniformly over its cross section.Find the maximum magnetic field produced by this wire.

  1. $\dfrac{\mu _0 il}{2\pi R}$

  2. $\dfrac{8\mu _0l}{\pi R}$

  3. $\dfrac{\mu _0l}{4\pi R}$

  4. $\dfrac{2\mu _0l}{\pi R}$


Correct Option: A
Explanation:

Let the current $i$ is uniformly distributed throughout the wire.

$R$ is the radius of the cylindrical wire.
From Ampere's circuital law, $\phi B\times dl=B\times 2\pi l$ (where $l$ is a small part of the ring)
For maximum magnetic field, $B={ \mu  } _{ 0 }\dfrac { i{ l }^{ 2 } }{ R } \times \dfrac { 1 }{ 2\pi l } \ \quad \quad =\dfrac { { \mu  } _{ o }il }{ 2\pi R } $
 

Motion of charges is noting but :

  1. Electric current

  2. magnetic effect

  3. heating effect

  4. all of the above


Correct Option: D
Explanation:
Due to motion of charges through a conductor, the current of charges passing through its cross-section changes. It causes electric current $\left( ie. \dfrac{da}{dt}\right)$. Because of this current, heating effect and magnetic effect are produced in accordance with Joules and Bio Savaert's law resp.
Option $-D$ is correct.

A condenser is charged using a constant current. The ratio of the magnetic field at a distance of R/2 and R from the axis is (R the radius of plate)

  1. 1:1

  2. 2:1

  3. 1:2

  4. 1:4


Correct Option: C

The magnetic field at the origin due to a current element $i.\vec {dl}$ placed at a position $\vec r$ is

  1. $\dfrac {\mu _0i}{4\pi} \dfrac {\vec {dl}\times \vec r}{r^3}$

  2. $\dfrac {\mu _0i}{4\pi} \dfrac {\vec r\times \vec {dl}}{r^3}$

  3. $-\dfrac {\mu _0i}{4\pi} \dfrac {\vec r\times \vec {dl}}{r^3}$

  4. $-\dfrac {\mu _0i}{4\pi} \dfrac {\vec {dl}\times \vec r}{r^3}$


Correct Option: A,C
Explanation:

$B= \dfrac{\mu _0}{4\pi}i\dfrac{\vec{dl}\times  \vec{r}}{r^3}=-\dfrac{\mu _0}{4\pi}i\dfrac{\vec{r}\times  \vec{dl}}{r^3}$
since $\vec{dl}\times  \vec{r} = -(\vec{r}\times  \vec{dl})$
Options (A) and (C) are correct

The Biot-Savart's law in vector from is:

  1. $ d\overrightarrow { B } =\dfrac { \mu _ o }{ 4\pi } \dfrac { di\left( \overrightarrow { l } \times \overrightarrow { r } \right) }{ r^ 2 } $

  2. $ d\overrightarrow { B } =\dfrac { \mu _ o }{ 4\pi } \dfrac { i\left( \overrightarrow { dl } \times \overrightarrow { r } \right) }{ r^ 2 } $

  3. $ d\overrightarrow { B } =\dfrac { \mu _ o }{ 4\pi } \dfrac { i\left( \overrightarrow { r } \times \overrightarrow { dl } \right) }{ r^ 2 } $

  4. $ d\overrightarrow { B } =\dfrac { \mu _ o }{ 4\pi } \dfrac { i\left( \overrightarrow { dl } \times \overrightarrow { r } \right) }{ r^ 3 } $


Correct Option: B

Which of the following particles will deviate $(< \pi/2)$ maximum when they enter magnetic filed region perpendicularly with same velocity and travel same distance.

  1. $He^{}$

  2. Proton

  3. $\alpha-particle$

  4. $Li^{++}$


Correct Option: D

A stationary magnet does not intereact with 

  1. iron rod

  2. moving charge

  3. moving magnet

  4. stationary charge


Correct Option: C

Which of the following gives the value of magnitude field according to, Biot-Savart's law'

  1. $ \frac {i\triangle l sin \theta}{r^2} $

  2. $ \frac {\mu _o}{4 \pi} \frac {i \triangle l sin \theta}{r} $

  3. $ \frac {\mu _o}{4\pi} \frac {i \triangle l sin \theta}{r^2} $

  4. $ \frac {\mu _o}{4 \pi} i \triangle l sin \theta $


Correct Option: C

The magnetic filed (dB) due to smaller element (dl) at a distance $(\vec r)$ from element carrying current i, is

  1. $\displaystyle dB = \frac{\mu _0 i}{4 \pi} \left ( \frac{\vec{dl} \times \vec r}{r} \right )$

  2. $\displaystyle dB = \frac{\mu _0 i}{4 \pi} i^2 \left ( \frac{\vec{dl} \times \vec r}{r^2} \right )$

  3. $\displaystyle dB = \frac{\mu _0 i}{4 \pi} i^3 \left ( \frac{\vec{dl} \times \vec r}{2r^2} \right )$

  4. $\displaystyle dB = \frac{\mu _0}{4 \pi} i \left ( \frac{\vec{dl} \times \vec r}{r^3} \right )$


Correct Option: D
Explanation:
$dB=\dfrac { { \mu  } _{ 0 }i }{ 4\pi  } \int { \dfrac { \left( \overrightarrow { dl } \times \hat { r }  \right)  }{ { r }^{ 2 } }  } \\$

we know that=$\hat { r } =\dfrac { \overrightarrow { r }  }{ { r }} \\$

$dB=\dfrac { { \mu  } _{ 0 }i }{ { 4 }\pi  } \int { \dfrac { \left( \overrightarrow { dl } \times \overrightarrow { r }  \right)  }{ { r }^{ 3 } }  }$ 

A particle of mass M and charge Q moving with velocity $\vec v$ describe a circular path of radius R when subjected to a uniform transverse magnetic field of induction B. The work done by the field when the particle completes one full circle is

  1. $\displaystyle \left ( \frac{Mv^2}{R} \right ) 2 \pi R$

  2. $zero$

  3. $BQ2 \pi R$

  4. $BQv2 \pi R$


Correct Option: B
Explanation:

Upon completing a full circle net displacement is 0.
Work done by the magnetic field is 0 because the net displacement caused by the magnetic field is 0.

The magnetic field due to a current element is independent of :

  1. current through it

  2. distance from it

  3. its length

  4. nature of meterial


Correct Option: D
Explanation:

$B=\dfrac{\mu _o}{4\pi}\dfrac{i\overrightarrow{dl}\times\overrightarrow{r}}{r^3}$

So it depends on all three : current , distance and length
but not on nature of material

The magnetic field  $\overline{dB}$ due to a small current element dl at a distance $\vec{r}$ and carrying current ‘i’ is

  1. $\overline{dB}=\dfrac{\mu _{0}}{4\pi }i\left ( \dfrac{\overline{dl}\times \bar{r}}{r} \right )$

  2. $\overline{dB}=\dfrac{\mu _{0}}{4\pi }i^{2}\left ( \dfrac{\overline{dl}\times \bar{r}}{r^{2}} \right )$

  3. $\overline{dB}=\dfrac{\mu _{0}}{4\pi }i^{2}\left ( \dfrac{\overline{dl}\times \bar{r}}{r} \right )$

  4. $\overline{dB}=\dfrac{\mu _{0}}{4\pi }i\left ( \dfrac{\overline{dl}\times \bar{r}}{r^{3}} \right )$


Correct Option: D
Explanation:

Bio-savert law - apply directly the statement of law

Magnetic field at a point on the line of current carrying conductor is

  1. maximum

  2. infinity

  3. zero

  4. finite value


Correct Option: C
Explanation:

because angle between line and distance becomes zero.
$\therefore\overrightarrow{l}\times\widehat{r}$  becomes zero.

For a given distance from a current element, the magnetic induction is maximum at an angle measured with respect to axis of the current. The angle is :

  1. $\dfrac{3\pi}{ 4}$

  2. $\dfrac{\pi }{4}$

  3. $\dfrac{\pi} {2}$

  4. $2\pi $


Correct Option: C
Explanation:
Magnetic field due to small current element is given as 
$B=\dfrac{\mu _o}{4\pi}\dfrac{\vec{idl}\times \hat{r}} {r^2}$
$B=\dfrac{\mu _o}{4\pi}\dfrac{idlr \sin\theta}{r^3}$
$\sin\theta=1$     for     $\theta=\dfrac{\pi}{2}$

A proton is moving with velocity ${10}^{4}m/s$ parallel to the magentic field of intensity 5 tesla.The force on the proton is

  1. $8\times {10}^{-15}N$

  2. ${10}^{4}N$

  3. $1.6\times {10}^{-19}N$

  4. Zero


Correct Option: D
Explanation:

Answer is D.

The magnitude and direction of F depend on the velocity of the particle and on the magnitude and direction of the magnetic field B.
When a charged particle moves parallel to the magnetic field vector, the magnetic force acting on the particle is zero.
When the particles velocity vector makes any angle with the magneticfield, the magnetic force acts in a direction perpendicular to both v and B; that is, F is perpendicular to the plane formed by v and B.
The magnitude of the magnetic force is
$F=qvBsin\theta $
where $\theta $ is the smaller angle between v and B. From this expression, we see that F is zero when v is parallel or antiparallel to B or 180) and maximum when v is perpendicular to B.
In this case, as the proton moves parallel to the magnetic field, the force is zero.

The pattern of the magnetic field around a conductor due to an electric current flowing through it depends on

  1. amount of current flowing through the conductor

  2. amount of voltage supplied to the conductor

  3. size of conductor

  4. shape of the conductor


Correct Option: D
Explanation:
We know that;
$\vec B=\dfrac{\mu _0}{4\pi}\int { \dfrac { Idl\times {\vec  r  } }{ \left| { r }^{ 1 } \right| ^{ 3 } }  } $
Where, $\vec B$ is magnetic field, $\vec I$ is current.
Thus magnitude of $\vec B$ depend on I, but pattern of magnetic field depend on shape of conductor as the direction of magnetic field is obtained used Cut finger rule i.e, pointing right hand thumb in current direction, Curl fingers describes direction thus pattern.

A magnetic field due to a long straight wire carrying a current I is proportional to

  1. I

  2. $I^2$

  3. $I^3$

  4. $\sqrt{I}$


Correct Option: A
Explanation:

Magnetic field due to large wire is 

$B=\dfrac{\mu _o I}{2\pi r}$
$B\propto I$

The value of $\mu$ is $4 \pi \times {10}^{-7} H {m}^{-1}$.

  1. True

  2. False


Correct Option: A
Explanation:

The physical constant $μ _0$ commonly called the vacuum permeability, permeability of free space, ... In the reference medium of classical vacuum, μ0 has an exact defined value: .... The value of $μ _0$ was chosen such that the rmks unit of current is equal in size to the ampere in the emu system: μ0 is defined to be $4π × 10^{−7} H/m.$

The value of magnetic field due to a small element of current carrying conductor at a distance r and lying on the plane perpendicular to the element of conductor is

  1. Zero

  2. Maximum

  3. Inversely proportional to the current

  4. None of the above


Correct Option: B
Explanation:

The Biot Savart law is used for computing the resultant magnetic field B at position r generated by a steady current I.  According to it $B=\frac {\mu _0 I } {4\pi} \int \frac {I\vec{dl} \times \vec{r}} { r^3}$.
So magnetic field at a distance r and lying on the plane perpendicular ($\pi /2$)to the element of conductor is maximum .

The magnetic field due to current flowing in a ling straight conductor is directly proportional to the current and inversely proportional to the distance of the point of observation from the conductor. What is this law known as?

  1. Blonde-Rey law

  2. Biot-Savart's law

  3. Beer-Lambert law

  4. Ampere's law


Correct Option: B

A current of i ampere is flowing in an equilateral triangle of side a. The magnetic induction at the centroid will be?

  1. $\dfrac{\mu _i}{3\sqrt{3}\pi a}$

  2. $\dfrac{3\mu _i}{2\pi a}$

  3. $\dfrac{5\sqrt{2}\mu _i}{3\pi a}$

  4. $\dfrac{9\mu _i}{2\pi a}$


Correct Option: D
Explanation:
a = length of side of equilateral triangle 

r = perpendicular distance of each side from centroid $=\frac { \sqrt { 3a }  }{ 6 } $

θ = angle by each end of each side at centroid = 60

Using Biot-savart's law , magnetic field at the centroid by each side is given as 

$B=\frac { μ }{ 4π } \ast \frac { i }{ r } \ast (Sinθ+Sinθ)$

$B=\frac { μ }{ 4π } \left( \frac { i }{ \sqrt { 3 }  } \frac { a }{ 6 }  \right) (Sin60+Sin60)$

$B=\frac { μ }{ 4π } \left( \frac { 6i }{ \sqrt { 3a }  } \frac { \sqrt { 3 }  }{ 2 }  \right) $

$B=\frac { μ }{ 4π } \frac { 6i }{ a } $

total magnetic field by all three sides is given as 

$B''=3B=3\frac { μ }{ 4π } \frac { 6i }{ a } $

$B''=\frac { μ }{ 2π } \frac { 9i }{ a } $




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