Tag: field due to a current carrying conductor

Questions Related to field due to a current carrying conductor

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

physics moving charges and magnetism field due to a current carrying conductor magnetic field due to a straight current carrying conductor magnetic field lines due to current

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

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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:

physics moving charges and magnetism field due to a current carrying conductor magnetic field due to a straight current carrying conductor magnetic field lines due to current

  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 } $

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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.

physics moving charges and magnetism field due to a current carrying conductor magnetic field due to a straight current carrying conductor magnetic field lines due to current

  1. $He^{}$

  2. Proton

  3. $\alpha-particle$

  4. $Li^{++}$

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Correct Option: D

A stationary magnet does not intereact with 

physics moving charges and magnetism field due to a current carrying conductor magnetic field due to a straight current carrying conductor magnetic field lines due to current

  1. iron rod

  2. moving charge

  3. moving magnet

  4. stationary charge

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Correct Option: C

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

physics moving charges and magnetism field due to a current carrying conductor magnetic field due to a straight current carrying conductor magnetic field lines due to current

  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 $

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Correct Option: C

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

physics moving charges and magnetism field due to a current carrying conductor magnetic field due to a straight current carrying conductor magnetic field lines due to current

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

Show answer
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

physics moving charges and magnetism field due to a current carrying conductor magnetic field due to a straight current carrying conductor magnetic field lines due to current

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

  2. $zero$

  3. $BQ2 \pi R$

  4. $BQv2 \pi R$

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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.

Assertion: Magnetism is relativistic

Reason: When we move along with the charge, so that there is no motion relative to us, we find no magnetic field associated with the charge

physics moving charges and magnetism field due to a current carrying conductor magnetic field due to a straight current carrying conductor magnetic field lines due to current

  1. Both A and R are true and R is the correct explanation of A.

  2. Both A and R are true and R is not correct explanation of A.

  3. A is true, but R is false

  4. A is false, but R is true

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Correct Option: A
Explanation:

A magnetic field is a region around some magnetic material or some moving electric charge. Within it the force of magnetism acts. Thus Magnetism is the aspect of the combined electromagnetic force. Also, it refers to the physical phenomena caused by magnets.

A magnetic field can be produced by the moving electric charge. As, the motion of any object is always relative, therefore the magnetic field will also be relativistic in nature.

As the reason is the correct explanation for the assertion

Hence option A is correct.

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

physics moving charges and magnetism field due to a current carrying conductor magnetic field due to a straight current carrying conductor magnetic field lines due to current

  1. current through it

  2. distance from it

  3. its length

  4. nature of meterial

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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

physics moving charges and magnetism field due to a current carrying conductor magnetic field due to a straight current carrying conductor magnetic field lines due to current

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

Show answer
Correct Option: D
Explanation:

Bio-savert law - apply directly the statement of law