Electric Current

Find the force of interaction between the following, as shown in figure. 

Current density in a cylindrical wire of radius $R$ is given as $J\left\{\begin{array}{c}{J}_0\left(\frac{x}{R}-1\right)\text{ for }0\le x\le \frac{R}{2}\\ J_0\frac{x}{R}\text{ for }\frac{R}{2}\le x\le R\end{array}\right.$. The current following in the wire is

How many coulombs are provided by a current of $0.010 \mathrm{mA}$ in the calculator battery that can operate for $1000$ hours?

When one ampere current is passed through a $Cu$ wire for $10$ seconds, the number of electrons passing through it is

The current density in a cylindrical wire of radius $r=4.0 \mathrm{mm}$ is $1.0\times {10}^6{ \mathrm{A}}^2{ \mathrm{m}}^2$. The current through the outer portion of the wire between radial distances $\frac{r}{2}$ and $r$ is $x\pi \mathrm{A}$; where $x$ is

The current density in a cylindrical wire of radius $4 \mathrm{mm}$ is $4\times {10}^6 \mathrm{A} {\mathrm{m}}^{-2}$. The current through the outer portion of the wire between radial distances $\frac{R}{2}$ and $R$ is _____ $\pi \mathrm{A}$.

A flow of ${10}^7$ electrons per second in a conducting wire constitutes a current of

In hydrogen discharge tube, it is observed that through a given cross-section $5\times {10}^{16}$ electrons are moving from right to left and $5\times {10}^{16}$ protons are moving from left to right per second. The current(in $\mathrm{mA}$) in the discharge tube will be

Current flowing through a wire depends on time as $I=3t^2+2t+5.$ The charge flowing through the cross-section of the wire in time $t=0$ to $t=2 \mathrm{s}$ is 

The amount of charge $Q$ passed in time $t$ through a cross section of a wire is $Q=5t^2+3t+1.$ The value of current at time $t=5s$ is 

A current of $2 \mathrm{A}$ is established in a circuit containing an aluminium resistor of length $30 \mathrm{cm}$. If the area of cross-section of the resistor is $0.003 {\mathrm{cm}}^2$ at a point P.The current density at that point will be :

A cylindrical conductor has length $l$ and area of cross-section $A.$ Its conductivity changes with distance $\left(x\right)$ from one of its ends as $\sigma ={\sigma }_0\frac{l}{x}$ [${\sigma }_0$ is a constant]. The electric field inside the conductor as a function of $x$ is $\frac{k}{10} \mathrm{V} {\mathrm{m}}^{-1}$  when a cell of emf $V$ is connected across the ends. Find $k$. [Given that $l=10 \mathrm{m}, x=2 \mathrm{m},\mathit{ }V=10$ Volt.]

A steady current $I$ is set up in a wire whose cross-sectional area decreases in the direction of the flow of the current. Then, as we examine the narrowing region

Number of electrons passes through a wire in $2$ minutes is $2.25\times {10}^y$, if current passing through the wire is $300 \mathrm{mA}$. Find the value of $y$.

The current through an element is shown in the figure. Determine the total charge that passes through the element after  $t= 2 \mathrm{s}$ in Coulombs.

In the circuit element given here, if the potential at point $B\text{,} V_{\mathrm{B}}=0\text{,}$ then the potentials of $A$ and $D$ are given as,

The current through an element is shown in the figure. Determine the total charge that passes through the element after  $t= 2 \mathrm{s}$ in Coulombs.

The current through an element is shown in the figure. Determine the total charge that has passed through the element at $t=0 \mathrm{s}$ in Coulombs.

Number of electrons passes through a wire in $2$ minutes is $2.25\times {10}^y$, if current passing through the wire is $300 \mathrm{mA}$. Find the value of $y$.

A source of e.m.f. $E = 15 \mathrm{V}$and having negligible internal resistance is connected to a variable resistance so that the current in the circuit increases with time as $i = (1.2 t + 3).$ Then, the total charge that will flow in first five second will be