A thin rod is bent in the shape of a small circle of radius $'r'$. If the charge per unit length of the rod is $'\sigma ',$ and if the circle is rotated about its axis at the rate of $'n'$ rotation per second, the magnetic induction at a point on the axis at a large distance $'y'$ from the centre is
Diffcult
Download our app for free and get started
${{\text{B}}_y} = \frac{{{\mu _0}{\text{I}}{{\text{R}}^2}}}{{2{{\left( {{{\text{y}}^2} + {{\text{R}}^2}} \right)}^{3/2}}}} = \frac{{{\mu _0}{\text{I}}{{\text{R}}^2}}}{{2{{\text{y}}^3}}}({\text{forY}} > > > {\text{R}})$
$\left[\because I=\frac{q}{t}=\frac{\sigma(2 \pi R)}{t}=\sigma(2 \pi R) n\right]$
$\mathrm{B}_{\mathrm{y}}=\frac{\mu_{0} \sigma(2 \pi \mathrm{R}) \mathrm{nR}^{2}}{2 \mathrm{y}^{3}}=\frac{\mu_{0} \sigma \pi \mathrm{R}^{3} \mathrm{n}}{\mathrm{y}^{3}}$
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 horizontal overhead power line is at a height of $4\,m$ from the ground and carries a current of $100\,A$ from east to west. The magnetic field directly below it on the ground is $(\mu _0 = 4\pi \times 10^{-7}\,TmA^{-1})$View Solution
- 2View SolutionAn electron is travelling horizontally towards east. A magnetic field in vertically downward direction exerts a force on the electron along
- 3The ammeter has range $1\, ampere$ without shunt. the range can be varied by using different shunt resistances. The graph between shunt resistance and range will have the natureView Solution
- 4A square frame of side I carries a current $i$. The magnetic field at its centre is $B$. The same current is passed through a circular coil having the same perimeter as the square. The field at the centre of the circular coil is $B^{\prime}$. The ratio of $\frac{B}{B^{\prime}}$ isView Solution
- 5View SolutionA galvanometer can be used as a voltmeter by connecting a
- 6A long insulated copper wire is closely wound as a spiral of ' $N$ ' turns. The spiral has inner radius ' $a$ ' and outer radius ' $b$ '. The spiral lies in the $X-Y$ plane and a steady current ' $I$ ' flows through the wire. The $Z$-component of the magnetic field at the center of the spiral isView Solution
- 7In the given diagram a rod is rotating with angular velocity $\omega $. Mass of this rod is $m$ charge $q$ and length $l$ then find out magnetic moment of this rodView Solution
- 8An ammeter of $5\, ohm$ resistance can read $5 \,mA$. If it is to be used to read $100\, volts$, how much resistance is to be connected in series ............... $\Omega $View Solution
- 9The magnetic force acting on charged particle of charge $2\,\mu C$ in magnetic field of $2\, T$ acting in $y-$ direction , when the particle velocity is $\left( {2\hat i + 3\hat j} \right) \times {10^6}\,m{s^{ - 1}}$ isView Solution
- 10In following diagram there is a straight wire carrying a current $I.$ Consider a circular path with radius $(R)$ near it. It $\vec B_T$ is the tangential component of magnetic field then find the value of integral $\int {{{\vec B}_T}.\overrightarrow {dl} } $View Solution
