The magnetic field due to a current in a stra | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For a finite wire segment of length $L$ carrying current $I$, the magnetic field $B$ at a distance $r$ on its perpendicular bisector is given by t

Vedclass · Accepted Answer

decreases as $\frac{1}{r^{2}}$

Vedclass · Answer

(B) For a finite wire segment of length $L$ carrying current $I$, the magnetic field $B$ at a distance $r$ on its perpendicular bisector is given by the Biot-Savart law integration:$B = \frac{\mu_{0} I}{4 \pi r} (\sin 	heta_{1} + \sin 	heta_{2})$For a segment of length $L$, $\sin 	heta_{1} = \sin 	heta_{2} = \frac{L/2}{\sqrt{r^{2} + (L/2)^{2}}}$.Substituting this, we get $B = \frac{\mu_{0} I}{4 \pi r} \cdot \frac{L}{\sqrt{r^{2} + (L/2)^{2}}}$.Since $r >> L$, the denominator $\sqrt{r^{2} + (L/2)^{2}} \approx r$.Thus, $B \approx \frac{\mu_{0} I L}{4 \pi r^{2}}$.Therefore, the magnetic field decreases as $\frac{1}{r^{2}}$.

The magnetic field due to a current in a straight wire segment of length $L$ at a point on its perpendicular bisector at a distance $r$ $(r >> L)$ is:

Similar Questions

$A$ horizontal overhead powerline is at a height of $4\ m$ from the ground and carries a current of $100\ A$ from east to west. The magnetic field directly below it on the ground is: (Given: $\mu_0 = 4\pi \times 10^{-7} \, T \cdot m/A$)

Current through $ABC$ and $A^{\prime} B^{\prime} C^{\prime}$ is $I$. What is the magnetic field at $P$? $BP = PB^{\prime} = r$. (Here $C^{\prime} B^{\prime} PBC$ are collinear).

Two wires $A$ and $B$ are of lengths $40 \ cm$ and $30 \ cm$. $A$ is bent into a circle of radius $r$ and $B$ into an arc of radius $r$. $A$ current $i_1$ is passed through $A$ and $i_2$ through $B$. To have the same magnetic inductions at the centre, the ratio of $i_1: i_2$ is

The magnetic induction at the centre $O$ in the figure shown is

$A$ long straight wire of radius $a$ carries a steady current $i$. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at $a/2$ and $2a$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module