A spherical charged conductor has surface charge density $\sigma $ . The electric field on its surface is $E$ and electric potential of conductor is $V$ . Now the radius of the sphere is halved keeping the charge to be constant. The new values of electric field and potential would be
Medium
Download our app for free and get started
$\mathrm{E}=\frac{1}{4 \pi \varepsilon_{0}} \frac{\mathrm{q}}{\mathrm{R}^{2}}$
As $\mathrm{q}$ is constant, so $E \propto \frac{1}{R^{2}}$
Radius is halved. Therefore, electric field will becomes $4$ times or $4 \mathrm{\,E}.$
Further, $\quad \mathrm{V}=\frac{1}{4 \pi \varepsilon_{0}} \frac{\mathrm{q}}{\mathrm{R}}.$
As $\mathrm{q}$ is constant, so $\mathrm{V} \propto \frac{1}{\mathrm{R}}.$
Radius is halved, so potential will becomes two time or $2 \mathrm{\,V}.$
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
- 1Condenser $A$ has a capacity of $15\,\mu F$ when it is filled with a medium of dielectric constant $15$. Another condenser $B$ has a capacity of $1\,\mu F$ with air between the plates. Both are charged separately by a battery of $100\;V$. After charging, both are connected in parallel without the battery and the dielectric medium being removed. The common potential now is.....$V$View Solution
- 2Find the equivalent capacitance between $A$ and $B$.......$\mu f$View Solution
- 3In a region, the potential is represented by $V(x, y, z) = 6x - 8xy - 8y + 6yz$, where $V$ is in volts and $x, y, z$ are in metres. The electric force experienced by a charge of $2$ coulomb situated at point $( 1, 1, 1)$ isView Solution
- 4A parallel plate capacitor is charged to a potential difference of $100\,V$ and disconnected from the source of $emf$ . A slab of dielectric is then inserted between the plates. Which of the following three quantities change?View Solution
$(i)$ The potential difference
$(ii)$ The capacitance
$(iii)$ The charge on the plates
- 5In the circuit shown below $C_1=10 \,\mu F , C_2=C_3=20 \,\mu F$, and $C_4=40 \,\mu F$. If the charge on $C_1$ is $20 \,\mu C$ then potential difference between $X$ and $Y$ is ......... $V$View Solution
- 6On rotating a point charge having a charge $q$ around a charge $Q$ in a circle of radius $r$. The work done will beView Solution
- 7Two metal spheres of capacitance ${C_1}$ and ${C_2}$ carry some charges. They are put in contact and then separated. The final charges ${Q_1}$ and ${Q_2}$ on them will satisfyView Solution
- 8Six metallic plates each with a surface area of one side $A$, are placed at a distance $d$ from each other. The alternate plates are connected to points $P$ and $Q$ as shown in figure. The capacitance of the system isView Solution
- 9View SolutionThe vehicles carrying inflammable fluids usually have metallic chains touching the ground:
- 10A charged particle $q$ is shot towards another charged particle $Q$ which is fixed, with a speed $v$. It approaches $Q$ upto a closest distance $r$ and then returns. If $q$ were given a speed $2v$, the closest distances of approach would beView Solution
