Equal charges $q$ are placed at the four corners $A,\,B,\,C,\,D$ of a square of length $a$. The magnitude of the force on the charge at $B$ will be
Equal charges $q$ are placed at the four corners $A,\,B,\,C,\,D$ of a square of length $a$. The magnitude of the force on the charge at $B$ will be
- A
$\frac{{3{q^2}}}{{4\pi {\varepsilon _0}{a^2}}}$
- B
$\frac{{4{q^2}}}{{4\pi {\varepsilon _0}{a^2}}}$
- C
$\left( {\frac{{1 + 2\sqrt 2 }}{2}} \right)\frac{{{q^2}}}{{4\pi {\varepsilon _0}{a^2}}}$
- D
$\left( {2 + \frac{1}{{\sqrt 2 }}} \right)\frac{{{q^2}}}{{4\pi {\varepsilon _0}{a^2}}}$
Similar Questions
Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic forces are acting
Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic forces are acting
Four charge $Q _1, Q _2, Q _3$, and $Q _4$, of same magnitude are fixed along the $x$ axis at $x =-2 a - a ,+ a$ and $+2 a$, respectively. A positive charge $q$ is placed on the positive $y$ axis at a distance $b > 0$. Four options of the signs of these charges are given in List-$I$ . The direction of the forces on the charge q is given in List-$II$ Match List-$1$ with List-$II$ and select the correct answer using the code given below the lists.$Image$
List-$I$
List-$II$
$P.$ $\quad Q _1, Q _2, Q _3, Q _4$, all positive
$1.\quad$ $+ x$
$Q.$ $\quad Q_1, Q_2$ positive $Q_3, Q_4$ negative
$2.\quad$ $-x$
$R.$ $\quad Q_1, Q_4$ positive $Q_2, Q_3$ negative
$3.\quad$ $+ y$
$S.$ $\quad Q_1, Q_3$ positive $Q_2, Q_4$ negative
$4.\quad$ $-y$
Four charge $Q _1, Q _2, Q _3$, and $Q _4$, of same magnitude are fixed along the $x$ axis at $x =-2 a - a ,+ a$ and $+2 a$, respectively. A positive charge $q$ is placed on the positive $y$ axis at a distance $b > 0$. Four options of the signs of these charges are given in List-$I$ . The direction of the forces on the charge q is given in List-$II$ Match List-$1$ with List-$II$ and select the correct answer using the code given below the lists.$Image$
| List-$I$ | List-$II$ |
| $P.$ $\quad Q _1, Q _2, Q _3, Q _4$, all positive | $1.\quad$ $+ x$ |
| $Q.$ $\quad Q_1, Q_2$ positive $Q_3, Q_4$ negative | $2.\quad$ $-x$ |
| $R.$ $\quad Q_1, Q_4$ positive $Q_2, Q_3$ negative | $3.\quad$ $+ y$ |
| $S.$ $\quad Q_1, Q_3$ positive $Q_2, Q_4$ negative | $4.\quad$ $-y$ |
- [IIT 2014]
Consider three charges $q_{1}, q_{2}, q_{3}$ each equal to $q$ at the vertices of an equilateral triangle of side $l .$ What is the force on a charge $Q$ (with the same sign as $q$ ) placed at the centroid of the triangle, as shown in Figure
Consider three charges $q_{1}, q_{2}, q_{3}$ each equal to $q$ at the vertices of an equilateral triangle of side $l .$ What is the force on a charge $Q$ (with the same sign as $q$ ) placed at the centroid of the triangle, as shown in Figure
${F_g}$ and ${F_e}$ represents gravitational and electrostatic force respectively between electrons situated at a distance $10\, cm$. The ratio of ${F_g}/{F_e}$ is of the order of
${F_g}$ and ${F_e}$ represents gravitational and electrostatic force respectively between electrons situated at a distance $10\, cm$. The ratio of ${F_g}/{F_e}$ is of the order of
Two small conducting spheres of equal radius have charges $ + 10\,\mu C$ and $ - 20\,\mu C$ respectively and placed at a distance $R$ from each other experience force ${F_1}$. If they are brought in contact and separated to the same distance, they experience force ${F_2}$. The ratio of ${F_1}$ to ${F_2}$ is
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