\(X\) and \(Y\) are large, parallel conducting plates close to each other. Each face has an area \(A.\) \(X\) is given a charge \(Q.\) \(Y\) is without any charge. Points \(A,B,\) and \(C\) are as shown in the figure. The incorrect option is:

          

1.	the field at \(B\) is \(Q \over2ε_0A\)	2.	the field at \(B\) is \(Q\overε_0A\)
3.	the fields at  \(A\), \(B\), and \(C\) are of the same magnitude	4.	the fields at \(A\) and \(C\) are of the same magnitude but in opposite directions

Four charges are arranged at the corners of a square ABCD, as shown in the adjoining figure. The force on the charge kept at the centre O is 

(1) Perpendicular to side BC

(2) Along the diagonal AC

(3) Along the diagonal BD

(4) Perpendicular to side AB

Three charges 4q, Q, and q are in a straight line in the position of 0, l/2, and l respectively. The resultant force on q will be zero if Q = 

(1) – q

(2) –2q

(3) $-\frac{q}{2}$

(4) 4q

Force of attraction between two point charges Q and – Q separated by d meter is F_e. When these charges are placed on two identical spheres of radius R = 0.3 d whose centres are d meter apart, the force of attraction between them is 

(1) Greater than F_e

(2) Equal to F_e

(3) Less than F_e

(4) Less than F_e

When 10¹⁹ electrons are removed from a neutral metal plate, the electric charge on it is 

(1) –1.6 C

(2) +1.6 C

(3) 10⁺¹⁹ C

(4) 10^–19 C

Three charges are placed at the vertices of an equilateral triangle of side \(a\) as shown in the following figure. The force experienced by the charge placed at the vertex \(A\) in a direction normal to \(BC\) is: 

1. \(Q^{2} / \left(\right. 4 \pi \epsilon_{0} a^{2} \left.\right)\)

2. \(- Q^{2} / \left(\right. 4 \pi \epsilon_{0} a^{2} \left.\right)\)

3. zero

4. \(Q^{2} / \left(\right. 2 \pi \epsilon_{0} a^{2} \left.\right)\)

Two particles of equal mass m and charge q are placed at a distance of 16 cm. They do not experience any force. The value of $\frac{q}{m}$ is 

(1) l

(2) $\sqrt{\frac{\pi {\epsilon }_0}{G}}$

(3) $\sqrt{\frac{G}{4\pi {\epsilon }_0}}$

(4) $\sqrt{4\pi {\epsilon }_{0}G}$

Two identical conductors of copper and aluminium are placed in an identical electric field. The magnitude of induced charge in the aluminium will be:

1. zero.

2. greater than in copper.

3. equal to that in copper.

4. less than in copper.

ABC is an equilateral triangle. Charges +q are placed at each corner. The electric intensity at O will be 

(1) $\frac{1}{4\pi {\epsilon }_0}\frac{q}{r^2}$

(2) $\frac{1}{4\pi {\epsilon }_0}\frac{q}{r}$

(3) Zero

(4) $\frac{1}{4\pi {\epsilon }_0}\frac{3q}{r^2}$

A charge particle is free to move in an electric field. It will travel 

(1) Always along a line of force

(2) Along a line of force, if its initial velocity is zero

(3) Along a line of force, if it has some initial velocity in the direction of an acute angle with the line of force

(4) None of the above