The magnitude of magnetic induction at mid-point $O$ due to current arrangement as shown in Fig will be
JEE MAIN 2023, Medium
Download our app for free and get started
Magnetic field due to current in $BC$ and $ET$ are outward at point ' $O$ '
$B _0=\frac{\mu_0 i }{4 \pi r }+\frac{\mu_0 i }{4 \pi r }=\frac{\mu_0 i }{2 \pi r }=\frac{\mu_0 i }{\pi a }$
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 Helmholtz coil has pair of loops, each with $N$ turns and radius $R$. They are placed coaxially at distance $R$ and the same current $I$ flows through the loops in the same direction. The magnitude of magnetic field at $P$, midway between the centres $A$ and $C$, is given by (Refer to figure)View Solution
- 2A galvanometer $G$ deflects full scale when a potential difference of $0.50 $ $V$ is applied. The internal resistance of the galvanometer $r_g$ is $25$ $ohms$. An ammeter is constructed by incorporating the galvanometer and an additional resistance $R_S$. The ammeter deflects full scale when a measurement of $2.0$ $A$ is made. The resistance $R_S$ is closest to : ................. $\Omega$View Solution
- 3A circular coil of wire carries a current. $PQ$ is a part of a very long wire carrying a current and passing close to the circular coil. If the directions of currents are those shown in figure, what is the direction of force acting on $PQ$ ?View Solution
- 4In an ionised sodium atom, an electron is moving in a circular path of radius $r$ with angular velocity $\omega $. The magnetic induction in $wb/m^2$ produced at the nucleus will beView Solution
- 5A long, straight wire of radius $a$ carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance $\frac{a}{3}$ and $2 a,$ respectively from the axis of the wire isView Solution
- 6Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields $\vec{E}=E_0 \hat{j}$ and $\vec{B}=B_0 \hat{j}$. At time $t=0$, this charge has velocity $\nabla$ in the $x$-y plane, making an angle $\theta$ with $x$-axis. Which of the following option$(s)$ is(are) correct for time $t>0$ ?View Solution
$(A)$ If $\theta=0^{\circ}$, the charge moves in a circular path in the $x-z$ plane.
$(B)$ If $\theta=0^{\circ}$, the charge undergoes helical motion with constant pitch along the $y$-axis.
$(C)$ If $\theta=10^{\circ}$, the charge undergoes helical motion with its pitch increasing with time, along the $y$-axis.
$(D)$ If $\theta=90^{\circ}$, the charge undergoes linear but accelerated motion along the $y$-axis.
- 7A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of $10\, A$. The magnetic field at point $O$ will be close toView Solution
- 8For a moving coil galvanometer, the deflection in the coil is $0.05\,rad$ when a current of $10\,mA$ is passed through it. If the torsional constant of suspension wire is $4.0 \times 10^{-5}\,Nm\,rad ^{-1}$, the magnetic field is $0.01\,T$ and the number of turns in the coil is $200$,the area of each turn (in $cm ^2$ ) is :View Solution
- 9A particle of mass $m = 1.67 \times 10^{-27}\, kg$ and charge $q = 1.6 \times 10^{-19} \, C$ enters a region of uniform magnetic field of strength $1$ $tesla$ along the direction shown in the figure. If the direction of the magnetic field is along the outward normal to the plane of the paper, then the time spent by the particle in the region of the magnetic field after entering it at $C$ is nearly :-......$ns$View Solution
- 10A charged particle going around in a circle can be considered to be a current loop. A particle of mass $m$ carrying charge $q$ is moving in a plane with speed $v$ under the influence of magnetic field $\overrightarrow{ B }$. The magnetic moment of this moving particleView Solution