A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of the resulting system 

1. increases by a factor of 4

2.decreases by a factor of 2

3. remain the same 

4. increases by a factor of 2

The diagrams below show regions of equipotentials.

An electric dipole is place at an angle of \(30^{\circ}\) with an electric field intensity \(2\times10^{5}~\text{N/C}\). It experiences a torque equal to \(4~\text{Nm}\). The charge on the dipole, if the dipole length is \(2~\text{cm}\), is: 

A parallel-plate capacitor of area A, plate separation d, and capacitance C is filled with four dielectric materials having dielectric constants $k_1,k_2,k_3$ $$and $k_4$ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by

(a) $\mathrm{k}={\mathrm{k}}_1+{\mathrm{k}}_2+{\mathrm{k}}_3+3{\mathrm{k}}_4$

(b) $k=\frac{2}{3}\left(k_1+k_2+k_3\right)+2k_4$

(c) $\frac{1}{k}=\frac{3}{2\left(k_1+k_2+k_3\right)}+\frac{1}{2k_4}$

(d) $\frac{1}{\mathrm{k}}=\frac{1}{{\mathrm{k}}_1}+\frac{1}{{\mathrm{k}}_2}+\frac{1}{{\mathrm{k}}_3}+\frac{3}{2{\mathrm{k}}_4}$

A capacitor of \(2~\mu\text{F}\) is charged as shown in the figure. When the switch \(S\) is turned to position \(2\), the percentage of its stored energy dissipated is:
         

If potential (in volts) in a region is expressed as V(x,y,z)=6xy-y+2yz, the electric field (in N/C) at point (1,1,0) is       

(1)-(3$\hat{i}$+5$\hat{j}$+3$\hat{\mathrm{k}}$)

(2)-(6$\hat{i}$+5$\hat{j}$+2$\hat{\mathrm{k}}$)

(3)-(2$\hat{i}$+3$\hat{j}$+$\hat{\mathrm{k}}$)

(4)-(6$\hat{i}$+9$\hat{j}$+$\hat{\mathrm{k}}$) 

Two thin dielectric slabs of dielectric constants K₁&K₂ ($K_1<K_2$) are inserted between plates of a parallel capacitor, as shown in the figure. The variation of electric field E between the plates with distance d as measured from plate P is correctly shown by  

1.

2. 

3.

4.

A conducting sphere of radius R is given a charge Q. The electric potential and field at the centre of the sphere respectively are

(a) zero and Q/4π$\epsilon$_oR² 

(b)Q/4π$\epsilon$_oR and zero

(c)Q/4π$\epsilon$_oR and Q/4π$\epsilon$_oR²

(d)Both are zero

In a region, the potential is represented by V(x,y,z)=6x-8xy-8y+6yz, where V is in volts and x,y,z are in meters. The electric force experienced by a charge of 2 coulomb situated at point (1,1,1) is

(1)6√5N

(2)30N

(3)24N

(4)4√35N