Two point charges $100\,\mu \,C$ and $5\,\mu \,C$ are placed at points $A$ and $B$ respectively with $AB = 40\,cm$. The work done by external force in displacing the charge $5\,\mu \,C$ from $B$ to $C$, where $BC = 30\,cm$, angle $ABC = \frac{\pi }{2}$ and $\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}\,N{m^2}/{C^2}$.........$J$
Diffcult
Download our app for free and get started
(d) Work done in displacing charge of $5\, µC$ from $B$ to $C $ is
$W = 5 \times {10^{ - 6}}\,({V_C} - {V_B})$ where
${V_B} = 9 \times {10^9} \times \frac{{100 \times {{10}^{ - 6}}}}{{0.4}} = \frac{9}{4} \times {10^6}\,V$
and ${V_C} = 9 \times {10^9} \times \frac{{100 \times {{10}^{ - 6}}}}{{0.5}} = \frac{9}{5} \times {10^6}\,V$
So $W = 5 \times {10^{ - 6}} \times \left( {\frac{9}{5} \times {{10}^6} - \frac{9}{4} \times {{10}^6}} \right) = - \frac{9}{4}\,J$
$W = 5 \times {10^{ - 6}}\,({V_C} - {V_B})$ where
${V_B} = 9 \times {10^9} \times \frac{{100 \times {{10}^{ - 6}}}}{{0.4}} = \frac{9}{4} \times {10^6}\,V$
and ${V_C} = 9 \times {10^9} \times \frac{{100 \times {{10}^{ - 6}}}}{{0.5}} = \frac{9}{5} \times {10^6}\,V$
So $W = 5 \times {10^{ - 6}} \times \left( {\frac{9}{5} \times {{10}^6} - \frac{9}{4} \times {{10}^6}} \right) = - \frac{9}{4}\,J$
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 charge of $10 \,\mu C$ is placed at the origin of $x-y$ coordinate system. The potential difference between two points $(0, a)$ and $(a, 0)$ in volt will beView Solution
- 2The electrostatic force between the metal plates of an isolated parallel plate capacitor $C$ having a charge $Q$ and area $A,$ isView Solution
- 3As shown in the figure, two parallel plate capacitors having equal plate area of $200\,cm ^2$ are joined in such a way that $a \neq b$. The equivalent capacitance of the combination is $x \varepsilon_0 F$. The value of $x$ is $..........$.View Solution
- 4The variation of electrostatic potential with radial distance $r$ from the centre of a positively charged metallic thin shell of radius $R$ is given by the graphView Solution
- 5A parallel plate capacitor Air filled with a dielectric whose dielectric constant varies with applied voltage as $K = V$. An identical capacitor $B$ of capacitance $C_0$ with air as dielectric is connected to voltage source $V_0 = 30\,V$ and then connected to the first capacitor after disconnecting the voltage source. The charge and voltage on capacitor.View Solution
- 6Potential difference between centre $\&$ the surface of sphere of radius $R$ and uniform volume charge density $\rho$ within it will be :View Solution
- 7Four capacitors are connected as shown in the figure. Their capacities are indicated in the figure. The effective capacitance between points $x$ and $y$ is (in $\mu F$)View Solution
- 8What is the effective capacitance between $A$ and $B$ in the following figure........$\mu \,F$View Solution
- 9A parallel plate capacitor of plate area $A$ and plate seperation $d$ is charged to potential difference $V$ and then the battery is disconnected. Aslab of dielectric constant $K$ is then inserted between the plates of the capacitor so as to fill the space between the plates. If $Q, E$ and $W$ denote respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted) and the work done on the system, in question, in the process of inserting the slab, thenView Solution
- 10Two capacitors of $3\,pF$ and $6\,pF$ are connected in series and a potential difference of $5000\,V$ is applied across the combination. They are then disconnected and reconnected in parallel. The potential between the plates isView Solution