A current of $i$ ampere is flowing in an equilateral triangle of side $a$. The magnetic induction at the centroid will be
Medium
Download our app for free and get started
(d)
$O$ is centroid and using the $\triangle O A D$ distance $O D=\frac{a}{2 \sqrt{3}}$
By all the three sides $AB , BC$ and $CA$, direction of magnetic field produced will be same and inward to the plane of paper
So $B_{\text {total }}=3\left[\frac{\mu_0 i}{4 \pi\left(\frac{a}{2 \sqrt{3}}\right)}\left(\sin 60^{\circ}+\sin 60^{\circ}\right)\right]=\frac{9 \mu_0 i}{2 \pi a}$
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 long straight wire carries a current of $35\, A$. What is the magnitude of the field $B$ at a point $20\, cm$ from the wire ?View Solution
- 2A conducting ring of mass $2\,\, kg$ and radius $0.5\,\ m$ is placed on a smooth horizontal plane. The ring carries a current $i = 4A. A$ horizontal magnetic field $B = 10T$ is switched on at time $t = 0$ as shown in figure. The initial angular acceleration of the ring will beView Solution
- 3A current $i$ ampere flows along the inner conductor of a coaxial cable and returns along the outer conductor of the cable, then the magnetic induction at any point outside the conductor at a distance $r$ metre from the axis isView Solution
- 4A beam of ions with velocity $2 \times {10^5}\,m/s$ enters normally into a uniform magnetic field of $4 \times {10^{ - 2}}\,tesla$. If the specific charge of the ion is $5 \times {10^7}\,C/kg$, then the radius of the circular path described will be.......$m$View Solution
- 5One metre length of wire carries a constant current. The wire is bent to form a circular loop. The magnetic field at the centre of this loop is $B$. The same is now bent to form a circular loop of smaller radius to have four turns in the loop. The magnetic field at the centre of this new loop isView Solution
- 6The deflection in moving coil galvanometer falls from $25$ divisions to $5$ division when a shunt of $24\ \Omega$ is applied. The resistance of galvanometer coil will be :View Solution
- 7A charge particle of charge $q$ and mass $m$ is accelerated through a potential diff. $V\, volts$. It enters a region of orthogonal magnetic field $B$. Then radius of its circular path will beView Solution
- 8The magnetic field $B$ with in the solenoid having $n$ $turns$ per $metre$ length and carrying a current of $i$ $ampere$ is given byView Solution
- 9A straight wire $AB$ of mass $40\,g$ and length $50\,cm$ is suspended by a pair of flexible leads in uniform magnetic field of magnitude $0.40\,T$ as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is ...........$A$. (Take $g=10\,ms ^{-2}$ ).View Solution
- 10An electron, a proton, a deuteron and an alpha particle, each having the same speed are in a region of constant magnetic field perpendicular to the direction of the velocities of the particles. The radius of the circular orbits of these particles are respectively $R_e, R_p, R_d \,$ and $\, R_\alpha$. It follows thatView Solution