A non-planar loop of conducting wire carrying a current $I$ is placed as shown in the figure. Each of the straight sections of the loop is of length $2a$. The magnetic field due to this loop at the point $P$ $(a,0,a)$ points in the direction
IIT 2001, Diffcult
Download our app for free and get started
(d) The magnetic field at $P(a,\,0,\,a)$ due to the loop is equal to the vector sum of the magnetic fields produced by loops $ABCDA$ and $AFEBA$ as shown in the figure.
Magnetic field due to loop $ABCDA$ will be along $\hat i$ and due to loop $AFEBA$, along $\hat k$. Magnitude of magnetic field due to both the loops will be equal. Therefore, direction of resultant magnetic field at $P$ will be $\frac{1}{{\sqrt 2 }}(\hat i + \hat k)$.
Magnetic field due to loop $ABCDA$ will be along $\hat i$ and due to loop $AFEBA$, along $\hat k$. Magnitude of magnetic field due to both the loops will be equal. Therefore, direction of resultant magnetic field at $P$ will be $\frac{1}{{\sqrt 2 }}(\hat i + \hat k)$.
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
- 1An electron moves in a circular orbit with a uniform speed $v$. It produces a magnetic field $B$ at the centre of the circle. The radius of the circle is proportional toView Solution
- 2A 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
- 3A charge moving with velocity $v$ in $X$-direction is subjected to a field of magnetic induction in the negative $X$-direction. As a result, the charge willView Solution
- 4View SolutionCyclotron is used to accelerate
- 5Two straight horizontal parallel wires are carrying the same current in the same direction, $d$ is the distance between the wires. You are provided with a small freely suspended magnetic needle. At which of the following positions will the orientation of the needle be independent of the magnitude of the current in the wiresView Solution
- 6Due to $10\, ampere$ of current flowing in a circular coil of $10\, cm$ radius, the magnetic field produced at its centre is $3.14 \times {10^{ - 3}}\,Weber/{m^2}$. The number of turns in the coil will beView Solution
- 7View SolutionThe direction of magnetic lines of forces close to a straight conductor carrying current will be
- 8View SolutionA magnetic field
- 9A circular loop of radius $0.0157\,m$ carries a current of $2.0\, amp$. The magnetic field at the centre of the loop is$({\mu _0} = 4\pi \times {10^{ - 7}}\,weber/amp - m)$View Solution
- 10A positive charge $'q'$ of mass $'m'$ is moving along the $+ x$ axis. We wish to apply a uniform magnetic field $B$ for time $\Delta t$ so that the charge reverses its direction crossing the $y$ axis at a distance $d.$ ThenView Solution