The charge per unit length of the four quadrants of the ring are $2\lambda$,$-2\lambda$,$\lambda$,and $-\lambda$ respectively. The electric field at the centre is

An inclined plane making an angle $30^{\circ}$ with the horizontal is placed in a uniform horizontal electric field of $100 \ Vm^{-1}$ as shown in the figure. $A$ small block of mass $1 \ kg$ and charge $0.01 \ C$ is allowed to slide down from rest from a height $h=1 \ m$. If the coefficient of friction is $0.2$,then the acceleration of the block is nearly,
(Acceleration due to gravity,$g=10 \ ms^{-2}$) (in $ms^{-2}$)

Ten charges are placed on the circumference of a circle of radius $R$ with constant angular separation between successive charges. Alternate charges $1, 3, 5, 7, 9$ have charge $(+q)$ each, while $2, 4, 6, 8, 10$ have charge $(-q)$ each. The potential $V$ and the electric field $E$ at the centre of the circle are respectively (Take $V = 0$ at infinity).

Two charged particles,each of mass $3 \ g$ and charge $0.2 \ \mu C$,stay in (vacuum) equilibrium on a horizontal surface with a separation of $20 \ cm$. The coefficient of friction is $\left[\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \ Nm^2 C^{-2}\right]$ and $\left(g=10 \ ms^{-2}\right)$.

Charges are placed on the vertices of a square as shown. Let $\vec E$ be the electric field and $V$ be the potential at the centre. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively,then

$A$ particle of mass $m$ and charge $q$ is kept at the top of a fixed frictionless sphere. $A$ uniform horizontal electric field $E$ is switched on. The particle loses contact with the sphere when the line joining the center of the sphere and the particle makes an angle $45^{\circ}$ with the vertical. The ratio $\frac{qE}{mg}$ is: