For a cylinder of radius $R$ current density $J =J_0 \frac{r}{R} $, where $J_0$ is a constant and $r$ is distance from axis. Calculate total current
Medium
Download our app for free and get started
$\mathrm{dI}=\mathrm{J} .2 \pi \mathrm{r} \mathrm{dr}$
$=\frac{\mathrm{J}_{0} \mathrm{r}}{\mathrm{R}} \times 2 \pi \mathrm{dr}$
$\mathrm{I}=\frac{\mathrm{J}_{0} 2 \pi}{\mathrm{R}} \int_{0}^{\mathrm{R}} \mathrm{r}^{2} \mathrm{dr}=\frac{2 \pi \mathrm{J}_{0}}{\mathrm{R}} \times \frac{\mathrm{R}^{3}}{3}=\frac{2}{3} \mathrm{J}_{0} \cdot \pi \mathrm{R}^{2}$
$=\frac{2}{3} J_{0} A$
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
- 1The figure shows a meter-bridge circuit, with $AB = 100\, cm$,$ X = 12\,\Omega$ and $R = 18\,\Omega$ , and the jockey $J$ in the position of balance. If $R$ is now made $8\,\Omega$ , through what distance will $J$ have to be moved to obtain balance? .............. $cm$View Solution
- 2By what percentage will the illumination of the lamp decrease if the current drops by $20 \%$ ?View Solution
- 3In the circuit shown here, $E_1 = E_2 = E_3 = 2 V$ and $R_1 = R_2 = 4\,ohms$. The current flowing between points $A$ and $B$ through battery $E_2$ isView Solution
- 4In a meter bridge experiment $\mathrm{S}$ is a standard resistance. $\mathrm{R}$ is a resistance wire. It is found that balancing length is $l=25 \;\mathrm{cm} .$ If $\mathrm{R}$ is replaced by a wire of half length and half diameter that of $\mathrm{R}$ of same material, then the balancing distance $\left.l^{\prime} \text { (in } \mathrm{cm}\right)$ will now beView Solution
- 5The current density in a cylindrical wire of radius $4 \; mm$ is $4 \times 10^{6} \; Am ^{-2}$. The current through the outer portion of the wire between radial distance $\frac{R}{2}$ and $R$ is $\dots \; \pi A .$View Solution
- 6In the ladder network shown, current through the resistor $3\, \Omega$ is $0.25\,A$. The input voltage $'V'$ is equal to:- ........... $V$View Solution
- 7Two light bulbs in the circuit have rating $A\,[24\ V, 48\,W]$ and $B\,[24\ V, 36\,W]$ as shown.View Solution
- 8A $60\, watt$ bulb operates on $220\,V$ supply. The current flowing through the bulb isView Solution
- 9View SolutionLamps used for household lighting are connected in
- 10In the following $'I'$ refers to current and other symbols have their usual meaning, Choose the option that corresponds to the dimensions of electrical conductivityView Solution