A capacitor of capacity C₁ is charged upto V volt and then connected to an uncharged capacitor of capacity C₂. Then final potential difference across each will be 

(1) $\frac{C_{2}V}{C_1+C_2}$

(2) $\left(1+\frac{{\displaystyle C_2}}{{\displaystyle C_1}}\right)V$

(3) $\frac{C_{1}V}{C_1+C_2}$

(4) $\left(1-\frac{{\displaystyle C_2}}{{\displaystyle C_1}}\right)V$

Four identical capacitors are connected as shown in diagram. When a battery of 6 V is connected between A and B, the charge stored is found to be 1.5 μC. The value of C₁ is 

(1) 2.5 μF

(2) 15 μF

(3) 1.5 μF

(4) 0.1 μF

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 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

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

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

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 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

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

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