Embibe Experts Solutions for Chapter: Magnetic Effect of Current, Exercise 3: Exercise - 3

An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement (s) is/are true ?

A long insulated copper wire is closely wound as a spiral of$N$ turns. The spiral has inner radius $a$ and outer radius$b$. The spiral lies in the X-Y plane and a steady current I flows through the wire. The Z component of the magnetic field at the center of the spiral is

A loop carrying current I lies in the x-y plane as shown in the figure. the unit vector $\hat{\mathrm{k}}$ is coming out of the plane of the paper. the magnetic moment of the current loop is :

An infinitely long hollow conducting cylinder with inner radius $\mathrm{R}/2$and outer radius R carries a uniform current density along is length. The magnitude of the magnetic field, $|\overrightarrow{ \mathrm{B}} |$as a function of the radial distance r from the axis is best represented by :

A particle of mass $M$ and positive charge $Q$, moving with a constant velocity $\overrightarrow{u_1}=4 \hat{\mathrm{i}} {\mathrm{ms}}^{-1}$, enters a region of uniform static magnetic field, normal to the $x-y$ plane. The region of the magnetic field extends from $x=0$ to $x=L$ for all values of $y$. After passing through this region, the particle emerges on the other side after $10$ milliseconds with a velocity $\overrightarrow{u_2}=2\left(\sqrt{3}\mathrm{i}+\hat{\mathrm{j}}\right){\mathrm{ms}}^{-1}$. The correct statement(s) is (are)

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

A current I flows along the length of an infinitely long, straight thin walled pipe. Then 

A charged particle with charge $q$ enters a region of constant uniform and mutually orthogonal fields $\overrightarrow{E}$ and $\overrightarrow{B}$ with a velocity $\overrightarrow{v}$ perpendicular to both $\overrightarrow{E}$ and $\overrightarrow{B}$ and comes out without any change in magnitude or direction of $\overrightarrow{v}$. Then