Exercise#1

The figure shows two large, closely placed, parallel, nonconducting sheets with identical (positive) uniform surface charge densities, and a sphere with a uniform (positive) volume charge density. Four points marked as $1, 2, 3$ and $4$ are shown in the space in between. If $E_1, E_2, E_3$ and $E_4$ are the magnitude of net electric fields at these points respectively then:

Two similar very small conducting spheres having charges $40 \mu \mathrm{C}$ and $-20 \mu \mathrm{C}$ are some distance apart. Now they are touched and kept at the same distance. The ratio of the initial to the final force between them is:

The magnitude of the electric force on $2 \mu \mathrm{C}$ charge placed at the center $O$ of two equilateral triangles each of side $10 \mathrm{cm},$ as shown in the figure is $P.$ If charge $A, B, C, D, E$ and $F$ are $2 \mu \mathrm{C}, 2 \mu \mathrm{C}, 2 \mu \mathrm{C}, -2 \mu \mathrm{C}, -2 \mu \mathrm{C}, -2 \mu \mathrm{C}$, respectively, then the value of $P$ is:

There is a uniform electric field in $X$-direction. If the work done by external agent in moving a charge of $0.2 \mathrm{C}$ through a distance of $2$ $\mathrm{m}$ slowly along the line making an angle of $60°$ with $X$-direction is $4$ $\mathrm{J}$, then the magnitude of $E$ is:

Two equal positive charges are kept at points $A$ and $B.$ The electric potential, while moving from $A$ to $B$ along straight line:

A semicircular ring of radius $0.5 \mathrm{m}$ is uniformly charged with a total charge of $1.5\times {10}^{-9}$ $\mathrm{C}$. The electric potential at the center of this ring is:

When a charge of $3 \mathrm{C}$, is placed in a uniform electric field, it experiences a force of $3000 \mathrm{N}$. The potential difference between two points separated by a distance of $1 \mathrm{cm}$, along field within this field is:

A $5$ $\mathrm{C}$ charge experiences a constant force of $2000 \mathrm{N}$, when moved between two points separated by a distance of $2 \mathrm{cm}$ in a uniform electric field. The potential difference between these two points is: