Two parallel wires in the plane of the paper are distance $X _0$ apart. A point charge is moving with speed $u$ between the wires in the same plane at a distance $X_1$ from one of the wires. When the wires carry current of magnitude $I$ in the same direction, the radius of curvature of the path of the point charge is $R_1$. In contrast, if the currents $I$ in the two wires have direction opposite to each other, the radius of curvature of the path is $R_2$.
If $\frac{x_0}{x_1}=3$, the value of $\frac{R_1}{R_2}$ is.
IIT 2014, Advanced
Download our app for free and get started
$B _2=\frac{\mu_0 I }{2 \pi x _1}+\frac{\mu_0 I }{2 \pi\left( x - x _1\right)}$ (opposite )
$B_1=\frac{\mu_0 I }{2 \pi x _1}-\frac{\mu_0 I }{2 \pi\left( x - x _1\right)} \text { (same) }$
Case -$1$ When current is in the same direction
$B=B_1=\frac{3 \mu_0 I }{2 \pi x_0}-\frac{3 \mu_0 I }{4 \pi x _0}=\frac{3 \mu_0 I }{4 \pi x _0} $
$R _1=\frac{ mv }{ qB }$
Case-$2$ When current is in oposite direction
$B = B _2=\frac{9 \mu_0 I }{4 \pi x _0} $
$R _2=\frac{ mv }{ qB } $
$\frac{ R _1}{ R _2}=\frac{ B _2}{ B _1}=\frac{9}{3}=3$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A straight wire carrying a current $10\, A$ is bent into a semicircular arc of radius $5\, cm.$ The magnitude of magnetic field at the center isView Solution
- 2A particle of mass $0.6\, g$ and having charge of $25\, nC$ is moving horizontally with a uniform velocity ${\rm{1}}{\rm{.2}} \times {\rm{1}}{{\rm{0}}^{\rm{4}}}\,m{s^{ - 1}}$ in a uniform magnetic field, then the value of the magnetic induction is $(g = 10\,m{s^{ - 2}})$View Solution
- 3A particle of charge $q$ and mass $m$ moves in a circular orbit of radius $r$ with angular speed $\omega $. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends onView Solution
- 4A $2\, MeV$ proton is moving perpendicular to a uniform magnetic field of $2.5\, tesla$. The force on the proton isView Solution
- 5View SolutionIf an ammeter is connected in parallel to a circuit, it is likely to be damaged due to excess
- 6An orbital electron in the ground state of hydrogen has magnetic moment $\mu_1$. This orbital electron is excited to $3^{rd}$ excited state by some energy transfer to the hydrogen atom. The new magnetic moment of the electron is $\mu_2$ , thenView Solution
- 7View SolutionCyclotron is used to accelerate
- 8A magnetised wire of moment $3.14\,A-m^2$ is bent in the form of a semi-circle; then the new magnetic moment will be.....$A-m^2$View Solution
- 9Two metallic rings $\mathrm{A}$ and $\mathrm{B}$, identical in shape and size but having different resistivities $\rho_A$ and $\rho_B$, are kept on top of two identical solenoids as shown in the figure. When current $I$ is switched on in both the solenoids in identical manner, the rings $\mathrm{A}$ and $\mathrm{B}$ jump to heights $h_A$ and $h_B$, respectively, with $h_A>h_B$. The possible relation$(s)$ between their resistivities and their masses $m_A$ and $m_B$ is(are)View Solution
$(A)$ $\rho_A>\rho_B$ and $m_A=m_B$
$(B)$ $\rho_A<\rho_B$ and $m_A=m_B$
$(C)$ $\rho_A>\rho_B$ and $m_A > m_B$
$(D)$ $\rho_A<\rho_B$ and $m_A < m_B$
- 10View SolutionAn electron is travelling horizontally towards east. A magnetic field in vertically downward direction exerts a force on the electron along