To produce a uniform magnetic field directed parallel to a diameter of a cylindrical region, one can use the saddle coils illustrated in figure. The loops are wrapped over a somewhat flattened tube. Assume the straight sections of wire are very long. The end view of the tube shows how the windings are applied. The overall current distribution is the superposition of two overlapping,circular cylinders of uniformly distributed current, one toward you and one away from you. The current density $J$ is the same for each cylinder. The position of the axis of one cylinder is described by a position vector a relative to the other cylinder. The magnetic field inside the hollow tube is.
Advanced
Download our app for free and get started
By ampere circuital law
$\int \mathrm{B} \cdot \mathrm{d} \ell=\mu_{0} \mathrm{I}_{\mathrm{m}}$
$\mathrm{B} \cdot 2 \pi \mathrm{r}=\mu_{0} \mathrm{J} \mathrm{zr}^{2}$
$\mathrm{B}_{1}=\frac{\mu_{0} \mathrm{J}_{1}}{2}$
$\mathrm{B}_{2}=\frac{\mu_{0} \mathrm{J} \overrightarrow{\mathrm{r}}_{2}}{2}$
$B_{\text {net }}=\frac{\mu_{0} J\left(\vec{r}_{1}-\vec{r}_{2}\right)}{2}$
$B_{\text {net }}=\frac{\mu_{0} J a}{2}$
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
- 1View SolutionIn order to increase the sensitivity of a moving coil galvanometer, one should decrease
- 2A particle of charge $16\times10^{-16}\, C$ moving with velocity $10\, ms^{-1}$ along $x-$ axis enters a region where magnetic field of induction $\vec B$ is along the $y-$ axis and an electric field of magnitude $10^4\, Vm^{-1}$ is along the negative $z-$ axis. If the charged particle continues moving along $x-$ axis, the magnitude of $\vec B$ isView Solution
- 3A 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 directionView Solution
- 4The radius of a circular loop is $r$ and a current $i$ is flowing in it. The equivalent magnetic moment will beView Solution
- 5A semi circular arc of radius $r$ and a straight wire along the diameter, both are carrying same current $i.$ Find out magnetic force per unit length on the small element $P$, which is at the centre of curvature.View Solution
- 6A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass $m$ and radius $r$ and it is in a uniform vertical magnetic field $B_0$, as shown in the figure. Initially, it hangs vertically downwards, because of acceleration due to gravity $g$, on two conducting supports at $P$ and $Q$. When a current $/$ is passed through the loop, the loop turns about the line $P Q$ by an angle $\theta$ given byView Solution
- 7The resistance of a galvanometer is $25\, ohm$ and it requires $50\,\mu A$ for full deflection. The value of the shunt resistance required to convert it into an ammeter of $5\, amp$ isView Solution
- 8A square loop, carrying a steady current $I,$ is placed in a horizontal plane near a long straight conductor carrying a steady current $I_1$ at a distance $d$ from the conductor as shown in figure. The loop will experienceView Solution
- 9A galvanometer with its coil resistance $25\,\Omega $ requires a current of $1\,mA$ for its full deflection. In order to construct an ammeter to read up to a current of $2\,A,$ the approximate value of the shunt resistance should beView Solution
- 10A circular loop has a radius of $5\, cm$ and it is carrying a current of $0.1\, amp$. Its magnetic moment isView Solution