Four charges are placed on corners of a square as shown in figure having side of $5\,cm$. If $Q$ is one microcoulomb, then electric field intensity at centre will be
$1.02 \times {10^7}N/C$ upwards
$2.04 \times {10^7}N/C$ downwards
$2.04 \times {10^7}N/C$ upwards
$1.02 \times {10^7}N/C$ downwards
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 charge distribution along the semi-circular arc is non-uniform . Charge per unit length $\lambda $ is given as $\lambda = {\lambda _0}\sin \theta $ , with $\theta $ measured as shown in figure. $\lambda_0$ is a positive constant. The radius of arc is $R$ . The electric field at the center $P$ of semi-circular arc is $E_1$ . The value of $\frac{{{\lambda _0}}}{{{ \in _0}{E_1}R}}$ is
Four point charges $-q, +q, +q$ and $-q$ are placed on $y$ axis at $y = -2d$, $y = -d, y = +d$ and $y = +2d$, respectively. The magnitude of the electric field $E$ at a point on the $x -$ axis at $x = D$, with $D > > d$, will vary as
Equal charges $q$ are placed at the vertices $A$ and $B$ of an equilateral triangle $ABC$ of side $a$. The magnitude of electric field at the point $C$ is
Four equal positive charges are fixed at the vertices of a square of side $L$. $Z$-axis is perpendicular to the plane of the square. The point $z = 0$ is the point where the diagonals of the square intersect each other. The plot of electric field due to the four charges, as one moves on the $z-$ axis.