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

A parallel plate air capacitor has capacitance $C,$ the distance of separation between plates is $d$ and potential difference $V$ is applied between the plates. The force of attraction between the plates of the parallel plate air capacitor is:

A parallel plate air capacitor of capacitance $C$ is connected to a cell of emf $V$ and then disconnected from it. A dielectric slab of dielectric constant $K,$ which can just fill the air gap of the capacitor is now inserted in it. Which of the following is incorrect?

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

   

1.		2.
3.		4.

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

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 a point $(1,1,1)$ is:
1. $6\sqrt{5}~\text{N}$
2. $30~\text{N}$
3. $24~\text{N}$
4. $4\sqrt{35}~\text{N}$

$A$, $B$ and $C$ are three points in a uniform electric field. The electric potential is: 

     

1.	maximum at $B$
2.	maximum at $C$
3.	same at all the three points $A, B$ and $C$
4.	maximum at $A$

An electric dipole of moment $p$ is placed in an electric field of intensity $E.$ The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\theta = 90^{\circ}$, the torque and the potential energy of the dipole will respectively be:
1. $pE\text{sin}\theta, ~-pE\text{cos}\theta$
2. $pE\text{sin}\theta, ~-2pE\text{cos}\theta$
3. $pE\text{sin}\theta, ~2pE\text{cos}\theta$
4. $pE\text{cos}\theta, ~-pE\text{sin}\theta$

Four-point charges $-Q, -q, 2q~\text{and}~2Q$ are placed, one at each corner of the square. The relation between $Q$ and $q$ for which the potential at the center of the square is zero is:

Two metallic spheres of radii $1~\text{cm}$ and $3~\text{cm}$ are given charges of $-1\times 10^{-2}~\text{C}$ and $5\times 10^{-2} ~\text{C}$, respectively. If these are connected by a conducting wire, then the final charge on the bigger sphere is:
1. $3\times 10^{-2}~ \text{C}$
2. $4\times 10^{-2}~\text{C}$
3. $1\times 10^{-2}~\text{C}$
4. $2\times 10^{-2}~\text{C}$