Embibe Experts Solutions for Chapter: Magnetic Effects of Current and Magnetism, Exercise 1: AIPMT - 25th July 2015

Given below are two statements:

Statement I : Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element $\left(I\mathrm{d}l\right)$ of a current carrying conductor only.

Statement II : Biot-Savart's law is analogous to Coulomb's inverse square law of charge $q$, with the former being related to the field produced by a scalar source, $I\mathrm{d}l$ while the latter being produced by a vector source, $q$.

In light of above statements choose the most appropriate answer from the options given below:

A long solenoid of radius $1 \mathrm{mm}$ has $100 \mathrm{turns}$ per $\mathrm{mm}$. If $1 \mathrm{A}$ current flows in the solenoid, the magnetic field strength at the centre of the solenoid is:

From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is

An infinitely long straight conductor carries a current of $5\mathrm{A}$ as shown. An electron is moving with a speed of ${10}^5 \mathrm{m} {\mathrm{s}}^{-1}$ parallel to the conductor. The perpendicular distance between the electron and the conductor is $20 \mathrm{cm}$ at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

 A thick current carrying cable of radius $R$ carries current $I$ uniformly distributed across its cross-section. The variation of magnetic field $B\left(r\right)$ due to the cable with the distance $r$ from the axis of the cable is represented by:

A uniform conducting wire of length $12a$ and resistance $R$ is wound up as a current-carrying coil in the shape of,

(i) an equilateral triangle of side $a$.
(ii) a square of side $a$.
The magnetic dipole moments of the coil in each case respectively are:

In the product

$\overrightarrow{F}=q(\overrightarrow{v}\times \overrightarrow{B})$

$=q\overrightarrow{v}\times \left(B\hat{\mathrm{i}}+B\hat{\mathrm{j}}+B_0\hat{\mathrm{k}}\right)$

For $q=1$ and $\overrightarrow{v}=2\hat{\mathrm{i}}+4\hat{\mathrm{j}}+6\hat{\mathrm{k}}$ and $\overrightarrow{F}=4\hat{\mathrm{i}}-20\hat{\mathrm{j}}+12\hat{\mathrm{k}}$

What will be the complete expression for $\overrightarrow{B}$?

A wire of length $L$ metre carrying a current of $I$ ampere is bent in the form of a circle. Its magnetic moment is,