Embibe Experts Solutions for Exercise 9: Assignment

An electron (charge $-e,$ mass $m )$ enters a uniform magnetic field $\overrightarrow{B}=-B_0\hat{k}$ at $A$ with a speed $v_0$ at an angle $37°$ and leaves the field at $B$ with speed $v$ (see figure). Then choose the correct statement(s).

A rectangular loop carrying current $i$ is shown in the diagram. If the magnetic field in the region is $2B_0\hat{i}+B_0\widehat{ j},$ then choose the correct statement(s).

A circular loop of radius $R$ carries current $I$ and is parallel to the $x-y$ plane. A uniform external magnetic field $-B_0\hat{k}$ exists in the region. The maximum tension which the wire of the loop can withstand is $T_0.$ Then

A thick spherical shell with inner radius $2R$ and outer radius $4R$ has uniform charge density $\rho .$ The shell also has a spherical cavity of radius $R$ centered at $B.$ (see figure). Select the correct statement(s)

A thin insulated tightly wound wire forms a plane spiral of $N$ turns and carries current $I.$ The radii of inside and outside turns are a and $3a$ respectively. Then

In a region of space uniform magnetic field $B_0 \hat{j}$ and uniform electric field $E_0 \hat{j}$ exist. A particle of charge $q$ and mass $m$ is projected from the origin at time $t=0$ with velocity $V_0\hat{i}.$ Then

A small circular coil of radius $\text{'}r\text{'}$ and number of turns $\text{'}n\text{'}$ is placed at the centre of another big fixed circular coil of radius $\text{'}R\text{'}$ and number of turns $N.$ Initially the planes of two coils are transverse to each other. If equal current $I$ flows through each coil, then

Two circular rings each of radius $\text{'}a\text{'}$ are joined together such that their planes are perpendicular to each other as shown in figure. (circle with solid line representation in vertical plane and the other circle with dotted line representation is horizontal plane respectively) A very small loop of mass $m$ and radius $r$ carrying a current $I_0$ is placed in the plane of the paper at common centre of each ring. The loop can freely rotate about any of its diametric axis. Find the time period (in s) of loop for small oscillations $\left(ma=\frac{2\pi {\mu }_0{I}_0}{{\pi }^2}\right)·$ Resistances of each half ring is shown in figure.