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Moving Charges and Magnetism — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsMoving Charges and Magnetism4 Marks
Question
A magnetic field can be produced by moving, charges or electric currents. The basic equation governing the magnetic field due to a current distribution is the Biot-Savart law. Finding the magnetic field resulting from a current distribution involves the vector product, and is inherently a calculas problem when the distance from the current to the field point is continuously changing. According to this law, the magnetic field at a point due to a current element of length $\text{d}\vec{\text{I}}$ carrying current I, at a distance r from the element is $\text{dB}=\frac{\mu_0}{4\pi}\frac{\text{I}(\text{d}{\vec{\text{I}}\times\vec{\text{r}}})}{\text{r}^3}$Biot-Savart law has certain similarities as well as difference with Coloumb's law for electrostatic field e.g., there is an angle dependence in Biot-Savart law which is not present in electrostatic case.
  1. The direction of magnetic field $\text{d}\vec{\text{B}}$ due to a current element $\text{Id}\vec{\text{l}}$ at a point of distance $\vec{\text{r}}$ from it, when a current I passes through a long conductor is in the direction
  1. Of position vector $\vec{\text{r}}$ of the point.
  2. Of current element $\text{Id}\vec{\text{l}}$
  3. Perpendicular to both $\text{d}\vec{\text{l}}$ and $\vec{\text{r}}$
  4. Perpendicular to $\text{d}\vec{\text{l}}$ only.
  1. The magnetic field due to a current in a straight wire segment of length Lat a point on its perpendicular bisector at a distance r (r >> L)
  1. Decreases as $\frac{1}{\text{r}}$
  2. Decreases as $\frac{1}{\text{r}^2}$
  3. Decreases as $\frac{1}{\text{r}^3}$
  4. approaches a finite limit as $\text{r}\rightarrow\infty$
  1. Two long straight wires are set parallel to each other. Each carries a current i in the same direction and the separation between them is 2r. The intensity of the magnetic field midway between them is:
  1. $\mu_0\frac{\text{i}}{\text{r}}$
  2. $4\mu_0\frac{\text{i}}{\text{r}}$
  3. $\text{Zero}$
  4. $\mu_0\frac{\text{i}}{\text{4r}}$
  1. A long straight wire carries a current along the z-axis for any two points in the x - y plane. Which of the following is always false?
  1. The magnetic fields are equal.
  2. The directions of the magnetic fields are the same.
  3. The magnitudes of the magnetic fields are equal.
  4. The field at one point is opposite to that at the other point.
  1. Biot-Savart law can be expressed alternatively as:
  1. Coulomb's Law.
  2. Ampere's circuital law.
  3. Ohm's Law.
  4. Gauss's Law.
✓

Answer

  1. (c) Perpendicular to both $\text{d}\vec{\text{l}}$ and $\vec{\text{r}}$
Explanation:

According to Biot-Savart's law, the magnetic induction due to a current element is given by,

$\text{d}\vec{\text{B}}=\frac{\mu_0}{4\pi}\frac{\text{Id}\vec{\text{l}\times\text{r}}}{\text{r}^3}$

This is perpendicular to both $\text{d}\vec{\text{l}}$ and $\vec{\text{r}}.$
  1. (b) Decreases as
Explanation:

From Biot-savart's law, $\text{dB}=\frac{\mu_0}{4\pi}\frac{\text{Idl}}{\text{r}^2}\text{i.e. dB}\propto\frac{1}{\text{r}^2}$
  1. (c) $\text{Zero}$
Explanation:

$\text{B}=\frac{\mu_0}{2\pi}.\frac{\text{i}}{\text{r}}-\frac{\mu_0}{2\pi}.\frac{\text{i}}{\text{r}}=0$
  1. (a) The magnetic fields are equal.
  1. (b) Ampere's circuital law.
Explanation:

Biot-Savart law can be expressed alternatively as Ampere circuital law.

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