Download App

Magnetic Field due to a Current — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMagnetic Field due to a Current1 Mark
MCQ
The magnetic field at the origin due to a current element $\text{i}\text{d}\ \vec{\text{l}}$ placed at a position $\overrightarrow{\text{r}}$ is:
  1. $\frac{\mu_0\text{i}}{4\pi}\frac{\text{d}\overrightarrow{\text{l}}\times\overrightarrow{\text{r}}}{\text{r}^3}$
  2. $-\frac{\mu_0\text{i}}{4\pi}\frac{\overrightarrow{\text{r}}\times​​\text{d}\overrightarrow{\text{l}}}{\text{r}^3}$
  3. $\frac{\mu_0\text{i}}{4\pi}\frac{\overrightarrow{\text{r}}\times​​\text{d}\overrightarrow{\text{l}}}{\text{r}^3}$
  4. $-\frac{\mu_0\text{i}}{4\pi}\frac{\text{d}\overrightarrow{\text{l}}\times\overrightarrow{\text{r}}}{\text{r}^3}$
  • A
    Only $A$
  • ✓
    $A$ and $B$
  • C
    Only $C$
  • D
    $B$ and $D$
✓

Answer

Correct option: B.
$A$ and $B$
The magnetic field at the origin due to current element $\text{i}\text{d}\ \vec{\text{l}}$ placed at a position $\overrightarrow{\text{r}}$ is given by,
$\text{d}\overrightarrow{\text{B}}=\frac{\mu_0\text{i}}{4\pi}\frac{\overrightarrow{\text{r}}\times\text{d}\overrightarrow{\text{l}}}{\text{r}^3}$
According to the cross product property,
$\overrightarrow{\text{A}}\times\overrightarrow{\text{B}}=-\overrightarrow{\text{B}}\times\overrightarrow{\text{A}}$
$\Rightarrow\text{d}\overrightarrow{\text{B}}=-\frac{\mu_0\text{i}}{4\pi}\frac{\overrightarrow{\text{r}}\times\text{d}\overrightarrow{\text{l}}}{\text{r}^3}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Magnetic Field due to a Current→Magnetic Field due to a Current — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The average velocities of the objects $A$ and $B$ are $V_A$ and $V_B$, respectively. The velocities are related such that $V_A>V_B$. The position$-$time graph for this situation can be represented as:
→
Beats are produced by two waves given by $y_1 = a\,\, sin\,\,2000\,\, \pi t$ and $y_2 = a\,\, sin\,\, 2008\,\, \pi t$ . The number of beats heard per second is
→
Two particles are projected simultaneously in the same vertical plane, from the same point on ground, but with same speeds but at different angles $( < 90^o )$ to the horizontal. The path followed by one, as seen by the other, is
→
A solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature ${120^o}C$, then
→
Who gave theory of relativity?
→
A scooter is going round a circular road of radius $100 \,m$ at a speed of $10 \,m/s$. The angular speed of the scooter will be ......... $rad/s$
→
Consider two containers $A$ and $B$ containing identical gases at the same pressure, volume and temperature. The gas in container $A$ is compressed to half of its original volume isothermally while the gas in container $B$ is compressed to half of its original value adiabatically. The ratio of final pressure of gas in $B$ to that of gas in $A$ is
→
If the temperature increases, the modulus of elasticity
→
A particle is moving such that its position coordinates $(x, y)$  are

$(2\, m, 3 \,m)$ at time $t = 0$

$(6\,m,7\,m) ,$ at time $ t=2 \,s$ and

$ (13\,m,14\,m),$ at $ t=5\,s$.

Average velocity vector $\vec v_{av}$ from $ t=0$ to $t= 5 $ is

→
From the top of a tower of height $40\, m,$ a ball is projected upwards with a speed of $20\, m/s$ at an angle $30^o$ to the horizontal. The ball will hit the ground in time ........$s$ (Take $g = 10\, m/s^2$)
→