A charge q is placed at centre of line joining two equal charges Q . system of the three

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1. Electric Charges and Fields

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A charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium, if $q$ is equal to

$ - \frac{Q}{2}$

$ - \frac{Q}{4}$

$ + \frac{Q}{4}$

$ + \frac{Q}{2}$

Solution

Suppose in the following figure. equilibrium of charge $\mathrm{B}$ is considered. Hence for it's

equilibrium $\left|\mathrm{F}_{\mathrm{A}}\right|=\left|\mathrm{F}_{\mathrm{C}}\right|$

$\Rightarrow \frac{1}{4 \pi \varepsilon_{0}} \frac{\mathrm{Q}^{2}}{4 \mathrm{x}^{2}}=\frac{1}{4 \pi \varepsilon_{0}} \frac{\mathrm{qQ}}{\mathrm{x}^{2}} \Rightarrow \mathrm{q}=\frac{-\mathrm{Q}}{4}$

Short Trick : For such type of problem the magnitude of middle charge can be determined if either of the extreme charge is in equilibrium by using the following formula.

In charge $\mathrm{A}$ is in equilibrium then $\mathrm{q}=$ $-Q_{B}\left(\frac{x_{1}}{x}\right)^{2}$

In charge $\mathrm{B}$ is in equilibrium the $\mathrm{q}=-\mathrm{Q}_{\mathrm{A}}\left(\frac{\mathrm{x}_{2}}{\mathrm{x}}\right)^{2}$

If the whole system is in equilibrium then use either of the above formula.

Standard 12

Physics

Two condensers $C_1$ and $C_2$ in a circuit are joined as shown in figure. The potential of point $A$ is $V_1$ and that of $B$ is $V_2$. The potential of point $D$ will be

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Two identical parallel plate capacitor are placed in series and connected to a constant voltage source of $V_0\, volt$. If one of the capacitors is completely immersed in a liquid with dielectric constant $K$, the potential difference between the plates of the other capacitor will change to

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Which of the following is a volt :

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Two concentric spheres $A$ and $B$ are kept very near to each other. $A$ is negatively charged and $B$ is earthed. The true statement is

$(A)$ Charge on $B$ is zero
$(B)$ Potential at $B$ is zero
$(C)$ Charge is uniformly distributed on $A$
$(D)$ Charge is non uniformly distributed on $A$

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Consider the situation shown. The switch $S$ is opened for a long time and then closed. The charge flown through the battery when $S$ is closed

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A charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium, if $q$ is equal to

Solution

Similar Questions

Two condensers $C_1$ and $C_2$ in a circuit are joined as shown in figure. The potential of point $A$ is $V_1$ and that of $B$ is $V_2$. The potential of point $D$ will be

Two identical parallel plate capacitor are placed in series and connected to a constant voltage source of $V_0\, volt$. If one of the capacitors is completely immersed in a liquid with dielectric constant $K$, the potential difference between the plates of the other capacitor will change to

Which of the following is a volt :

Two concentric spheres $A$ and $B$ are kept very near to each other. $A$ is negatively charged and $B$ is earthed. The true statement is $(A)$ Charge on $B$ is zero $(B)$ Potential at $B$ is zero $(C)$ Charge is uniformly distributed on $A$ $(D)$ Charge is non uniformly distributed on $A$

Consider the situation shown. The switch $S$ is opened for a long time and then closed. The charge flown through the battery when $S$ is closed

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Two concentric spheres $A$ and $B$ are kept very near to each other. $A$ is negatively charged and $B$ is earthed. The true statement is

$(A)$ Charge on $B$ is zero
$(B)$ Potential at $B$ is zero
$(C)$ Charge is uniformly distributed on $A$
$(D)$ Charge is non uniformly distributed on $A$