A uniform electric field pointing in positive x-direction exists in a region. Let A be the origin, B be the point on the x-axis at x = +1 cm and C be the point on the y-axis at y = +1 cm. Then the potentials at the points A, B and C satisfy 

(1) V_A < V_B

(2) V_A > V_B

(3) V_A < V_C

(4) V_A > V_C

Electric potential is given by

$V=6x-8x{y}^2-8y+6yz-4z^2$

Then electric force acting on 2C point charge placed on origin will be 

(1) 2N

(2) 6N

(3) 8N

(4) 20N

The electric potential at a point (x, y) in the x – y plane is given by V = –kxy. The field intensity at a distance r from the origin varies as 

(1) r²

(2) r

(3) $\frac{1}{r}$

(4) $\frac{1}{r^2}$

A negatively charged plate has charge density of 2 × 10^–6 C/m². The initial distance of an electron which is moving toward plate but cannot strike the plate, if it is having energy of 200 eV 

(1) 1.77 mm

(2) 3.51 mm

(3) 1.77 cm

(4) 3.51 cm

Two identical thin rings each of radius R meters are coaxially placed at a distance R meters apart. If Q₁ coulomb and Q₂ coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of other is 

(1) Zero

(2) $\frac{q(Q_2-Q_1)(\sqrt{2}-1)}{\sqrt{2}.4\pi {\epsilon }_{0}R}$

(3) $\frac{q\sqrt{2}(Q_1+Q_2)}{4\pi {\epsilon }_{0}R}$

(4) $\frac{q(Q_1+Q_2)(\sqrt{2}+1)}{\sqrt{2}.4\pi {\epsilon }_{0}R}$

A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of –3Q, the new potential difference between the same two surfaces is 

(1) V

(2) 2V

(3) 4V

(4) –2V

Two equal point charges are fixed at x = –a and x = +a on the x-axis. Another point charge Q is placed at the origin. The change in the electrical potential energy of Q, when it is displaced by a small distance x along the x-axis, is approximately proportional to 

(1) x

(2) x²

(3) x³

(4) 1/x

Consider two points \(1\) and \(2\) in a region outside a charged sphere. Two points are not very far away from the sphere. If \(E\) and \(V\) represent the electric field vector and the electric potential, which of the following is not possible?

A non-conducting ring of radius 0.5 m carries a total charge of 1.11 × 10^–10 C distributed non-uniformly on its circumference producing an electric field $\overrightarrow{E}$ everywhere in space. The value of the line integral ${\int }_{l=\infty }^{l=0}-\overrightarrow{E}.\overrightarrow{dl}(l=0$ being centre of the ring) in volt is 

(1) + 2

(2) – 1

(3) – 2

(4) Zero