The three charges $q / 2, q$ and $q / 2$ are placed at the corners $A , B$ and $C$ of a square of side ' $a$ ' as shown in figure. The magnitude of electric field $(E)$ at the comer $D$ of the square, is
The three charges $q / 2, q$ and $q / 2$ are placed at the corners $A , B$ and $C$ of a square of side ' $a$ ' as shown in figure. The magnitude of electric field $(E)$ at the comer $D$ of the square, is
- [JEE MAIN 2022]
- A
$\frac{ q }{4 \pi \epsilon_{0} a ^{2}}\left(\frac{1}{\sqrt{2}}+\frac{1}{2}\right)$
- B
$\frac{ q }{4 \pi \in_{0} a ^{2}}\left(1+\frac{1}{\sqrt{2}}\right)$
- C
$\frac{ q }{4 \pi \epsilon_{0} a ^{2}}\left(1-\frac{1}{\sqrt{2}}\right)$
- D
$\frac{ q }{4 \pi \in_{0} a ^{2}}\left(\frac{1}{\sqrt{2}}-\frac{1}{2}\right)$
Similar Questions
The electric field due to a charge at a distance of $3\, m$ from it is $500\, N/coulomb$. The magnitude of the charge is.......$\mu C$ $\left[ {\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {{10}^9}\,\frac{{N - {m^2}}}{{coulom{b^2}}}} \right]$
The electric field due to a charge at a distance of $3\, m$ from it is $500\, N/coulomb$. The magnitude of the charge is.......$\mu C$ $\left[ {\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {{10}^9}\,\frac{{N - {m^2}}}{{coulom{b^2}}}} \right]$
A charged cork of mass $m$ suspended by a light string is placed in uniform electric filed of strength $E= $$(\hat i + \hat j)$ $\times$ $10^5$ $NC^{-1}$ as shown in the fig. If in equilibrium position tension in the string is $\frac{{2mg}}{{(1 + \sqrt 3 )}}$ then angle $‘\alpha ’ $ with the vertical is
A charged cork of mass $m$ suspended by a light string is placed in uniform electric filed of strength $E= $$(\hat i + \hat j)$ $\times$ $10^5$ $NC^{-1}$ as shown in the fig. If in equilibrium position tension in the string is $\frac{{2mg}}{{(1 + \sqrt 3 )}}$ then angle $‘\alpha ’ $ with the vertical is
The surface charge density of a thin charged disc of radius $R$ is $\sigma $. The value of the electric field at the centre of the disc is $\frac{\sigma }{{2\,{ \in _0}}}$. With respect to the field at the centre, the electric field along the axis at a distance $R$ from the centre of the disc
The surface charge density of a thin charged disc of radius $R$ is $\sigma $. The value of the electric field at the centre of the disc is $\frac{\sigma }{{2\,{ \in _0}}}$. With respect to the field at the centre, the electric field along the axis at a distance $R$ from the centre of the disc
- [JEE MAIN 2013]
A thin conducting ring of radius $R$ is given a charge $+Q.$ The electric field at the centre $O$ of the ring due to the charge on the part $AKB$ of the ring is $E.$ The electric field at the centre due to the charge on the part $ACDB$ of the ring is
A thin conducting ring of radius $R$ is given a charge $+Q.$ The electric field at the centre $O$ of the ring due to the charge on the part $AKB$ of the ring is $E.$ The electric field at the centre due to the charge on the part $ACDB$ of the ring is
- [AIPMT 2008]
A flat circular disc has a charge $ + Q$ uniformly distributed on the disc. A charge $ + q$ is thrown with kinetic energy $E$ towards the disc along its normal axis. The charge $q$ will
A flat circular disc has a charge $ + Q$ uniformly distributed on the disc. A charge $ + q$ is thrown with kinetic energy $E$ towards the disc along its normal axis. The charge $q$ will