Q147 / 160 · TS EAMCET 2023 (14 May Shift 1) · Physics

It is found that a non-zero current element is unable to produce any magnetic field at a particular point. Then the angle between the current element and the position vector of that point with respect to the current element is

  • A
    must be $45^{\circ}$
  • Correct answer
    B
    may be $0^{\circ}$ or $180^{\circ}$
  • C
    must be $90^{\circ}$
  • D
    may be $30^{\circ}$ or $60^{\circ}$

Solution

The Biot savant law is used for finding magnetic field $B$ at position $r$ generated by a Steady current $I$ is given by $$ \mathrm{B}=\frac{\mathrm{r}_{\mathrm{o}} \mathrm{I}}{4 \pi} \int \frac{\mathrm{Id} \overrightarrow{\mathrm{l}} \times \overrightarrow{\mathrm{r}}}{\mathrm{r}^3} \quad=\frac{\mu_0 \mathrm{I}}{4 \pi} \int \frac{\mathrm{Idl} \mathrm{r} \sin \theta}{\mathrm{r}^3} $$ If $\theta=0$ or 180 $$ \because B=0 $$

Hence, the correct answer is option: 'B'.

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