Embibe Experts Solutions for Chapter: Magnetic Effects of Current and Magnetism, Exercise 3: Level 3

The figure shows infinitely long bent wires in the plane of paper, each carrying a current $i$ with $O$ as origin and $x$ and $y$ axes as shown. The co-ordinates of points $P \text{and} Q$ are $(2 \mathrm{m}\text{,} 0)$ and $(6 \mathrm{m}\text{,} 0)$, respectively. The magnetic induction at $P$ is given by $\frac{\alpha {\mu }_{0}i}{32\pi }$. What is the value of $\alpha$?

A charged particle enters into a uniform magnetic field with velocity $v_0$ perpendicular to it, the length of magnetic field is $x=\frac{\sqrt{3}}{2}R$, where $R$ is the radius of the circular path of the particle in the field. The magnitude of change in velocity of the particle when it comes out of the field is

A rectangular region of dimensions $w\times I\left(w<<I\right)$ has a constant magnetic field into the plane of the paper as shown. On one side the region is bounded by a screen. On the other side positive ions of mass $m$ and charge $q$ are accelerated from rest and towards the screen by a parallel plate capacitor at constant potential difference $V<0$, and come out through a small hole in the upper plate. Which one of the following statements is correct regarding the charge on the ions that hit the screen? 

An electron moving with velocity $\overrightarrow{\mathrm{v}}=\hat{\mathrm{i}}{v}_{\mathrm{x}}$ enters a uniform magnetic field $\overrightarrow{\mathrm{B}}=\hat{\mathrm{k}}{B}_{\mathrm{z}}$. The electron experiences

A beam of protons with velocity $600 \mathrm{km} {\mathrm{s}}^{-1}$ enters a uniform magnetic field of $0.2 \mathrm{T}$. The velocity makes an angle of $30°$ with the magnetic field. The radius of the helical path will be

The maximum energy of a deuteron coming out a cyclotron is $20 \mathrm{MeV}$. The maximum energy of proton that can be obtained from this accelerator is

The correct curve between the magnetic induction $\left(B\right)$ along the axis of a long solenoid due to current flow $i$ in it and at a distance $x$ from one end is,

Two particles, each of mass $m$ and charge $q$ are attached to the two ends of a light rigid rod of length $2R$. The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is