Tag: magnetic field due to a straight current carrying conductor

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Multiple choice 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

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 } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Biot-Savart law in vector form gives the magnetic field dB due to a current element idL at position r. The correct expression has the cross product of current element vector dl and position vector r in the numerator, divided by r cubed in the denominator to make it dimensionally consistent as an inverse-square law in vector form.

Multiple choice 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

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. $Li^{++}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The radius of the path is r = mv / (qB). For the same velocity and distance, the particle with the smallest radius (highest q/m ratio) will deviate the most. Li++ has a higher charge-to-mass ratio than the others.

Multiple choice 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

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 $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Biot-Savart's law states that the magnetic field dB is proportional to i*dl*sin(theta)/r^2. The constant of proportionality is mu0/4pi.

Multiple choice 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

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. $\displaystyle dB = \frac{\mu _0}{4 \pi} i \left ( \frac{\vec{dl} \times \vec r}{r^3} \right )$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$dB=\dfrac { { \mu  } _{ 0 }i }{ 4\pi  } \int { \dfrac { \left( \overrightarrow { dl } \times \hat { r }  \right)  }{ { r }^{ 2 } }  } \\$

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

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

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. $BQv2 \pi R$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

Multiple choice 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

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

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice 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

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
Reveal answer Fill a bubble to check yourself
D Correct answer
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

Multiple choice 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

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. $\overline{dB}=\dfrac{\mu _{0}}{4\pi }i\left ( \dfrac{\overline{dl}\times \bar{r}}{r^{3}} \right )$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Bio-savert law - apply directly the statement of law