The electrostatic potential inside a charged spherical ball is given by $\phi = ar^2 + b$ where $r$ is the distance from the centre $a,\,b$ are constants. Then the charge density inside the ball is
$ - \,6a{\varepsilon _0}r$
$ - \,24\pi a{\varepsilon _0}$
$ - \,6a{\varepsilon _0}$
$ - \,24\pi a{\varepsilon _0}r$
Two opposite and equal charges $4 \times {10^{ - 8}}\, coulomb$ when placed $2 \times {10^{ - 2}}\,cm$ away, form a dipole. If this dipole is placed in an external electric field $4 \times 10^8\, newton / coulomb$ , the value of maximum torque and the work done in rotating it through $180^o$ will be
The electric potential $(V)$ as a function of distance $(x)$ [in meters] is given by $V = (5x^2 + 10 x -9)\, Volt$. The value of electric field at $x = 1\, m$ would be......$Volt/m$
A charged object is launched inside a time varying electric field. Its motion is recorded by a video camera on a video tape. When it is at a certain moment $A$ , its position vector $\vec r$, velocity $\vec v$ and acceleration $\vec a$ are measured. A student watches the video at a later time but mistakenly plays the tape in the reverse direction. What is the position, velocity, and acceleration of the object, at moment $A$ observed by the student respectively?
A parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a potential difference $V$ . Another capacitor of capacitance $2C$ is similarly charged to a potential difference $2V$ . The charging battery is now disconnected and the capacitors are connect in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is
Four capacitors of capacitance $10\, \mu\, F$ and a battery of $200\,V$ are arranged as shown. How much charge will flow through $AB$ after the switch $S$ is closed?