Electric Charges and Fields

Two point charges q1=3 μC and q2=-4 μC are placed at points (2 i+3 j+3 k ) and ( i+ j+ k ) respectively. Force on charge q2 is N. (Take 14 0=9 109 SI Units)

1. (12 i+24 j+24 k ) 10-3
2. (4 i+8 j+8 k ) 10-3
3. (3 i+6 j+6 k ) 10-3
4. (-4 i-8 j-8 k ) 10-3

A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb. If the magnitude of the electric field at centre of the half ring is 100 V/m, then the value of Q is nC. ( 0=8.85 10-12 C2/Nm2 and =3.14)

1. 2.14
2. 2.44
3. 3.25
4. 0.7

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field E1=E0 x. If another electric field E2=2E0 ( y+ z ) is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

1. 73%
2. 63%
3. 83%
4. 53%

Two short electric dipoles A and B having dipole moment p1 and p2 respectively are placed with their axes mutually perpendicular as shown in the figure. The resultant electric field at a point x is making an angle of 60 with the line joining points O and x. The ratio of the dipole moments p2/p1 is . [figure]

1. 32
2. 2 3
3. 1 3
4. 3

Two point charges 8 μC and -2 μC are located at x=2 cm and x=4 cm, respectively on the x-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is .

1. 4 : 1
2. 3 : 4
3. 4 : 3
4. 4 : 5

Identify the correct statements : Choose the correct answer from the options given below :

1. A, C, E Only
2. A, B, D, E Only
3. B, C, D, E Only
4. A, B, C, D Only

The electrostatic potential in a charged spherical region of radius r varies as V = ar3 + b, where a and b are constants. The total charge in the sphere of unit radius is a 0. The value of is . (permittivity of vacuum is 0)

1. -12
2. -8
3. -9
4. -6

Three charges +2q, +3q and -4q are situated at (0, -3a), (2a, 0) and (-2a, 0) respectively in the xy plane. The resultant dipole moment about origin is .

1. 2qa(7 i - 3 j)
2. 2qa(3 j - 7 i)
3. 2qa(3 i - 7 j)
4. 2qa(3 j - i)

A point charge q = 1 is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge Q = 24 , distributed uniformly along its length, as shown in figure. Force between q and wire is N. (Use : 14 0 = 9 109 N m2/C2) [figure]

Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is: [figure]

1. 3q2 0
2. 3q4 0
3. q 0
4. 3q 0

Two short dipoles (A, B), A having charges 2 and length 1 cm and B having charges 4 and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point P, equi-distant from the centres of both dipoles is N/C. [figure]

1. 916 2 105
2. 916 2 104
3. 9 2 104
4. 4.5 2 104

A simple pendulum has a bob with mass m and charge q. The pendulum string has negligible mass. When a uniform and horizontal electric field E is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is .

1. mg - qE
2. m2g2 + q2E2
3. mg + qE
4. m2g2 - q2E2

Six point charges are kept 60 apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the center of the circle is . ( 0 is permittivity of free space) [figure]

1. - ( 5Q8 0 R2 )( i - 3 j)
2. Q4 0 R2( 3 i - j)
3. - Q4 0 R2( 3 i - j)
4. - 5Q8 0 R2( i + 3 j)

An infinitely long wire has uniform linear charge density = 2 nC/m. The net flux through a Gaussian cube of side length 3 cm, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be x N m2 C-1, where x is: [Neglect any edge effects and use 14 0 = 9 109 SI units]

1. 6.48
2. 0.72
3. 1.44
4. 2.16

A dipole with two electric charges of 2 magnitude each, with separation distance 0.5 , is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30 from the axis, it tends to realign in the direction due to a torque. The value of torque is:

1. 2.5 10-9 Nm
2. 2.5 10-12 Nm
3. 5 10-3 Nm
4. 5 10-9 Nm

The electric field in a region is given by E = (2 i + 4 j + 6 k) 103 N/C. The flux of the field through a rectangular surface parallel to x–z plane is 6.0 Nm2C-1. The area of the surface is cm2.

Two infinite identical charged sheets and a charged spherical body of charge density ' ' are arranged as shown in figure. Then the correct relation between the electrical fields at A, B, C and D points is: [figure]

1. | EA | = | EB |; EC > ED
2. EA = EB; EC = ED
3. EC ED; EA > EB
4. EA > EB; EC = ED

Two small spherical balls of mass 10 g each with charges -2 and 2 , are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite non-conducting charge sheet with uniform charge density of 100 /m2 such that length of rod makes an angle of 30 with electric field generated by charge sheet. Net torque acting on the rod is: (Take 0 = 8.85 10-12 C2/Nm2)

1. 1.12 Nm
2. 2.24 Nm
3. 11.2 Nm
4. 112 Nm

A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB at 'O' is 'E' in magnitude. What would be the magnitude of electric field at 'O' due to arc ABC ? [figure]

1. 2E
2. Zero
3. E/2
4. 2E

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density + and -2 . The force experienced by a point charge +q placed at the mid point between two plates will be: [figure]

1. 3 q4 0
2. 3 q2 0
3. q4 0
4. q2 0

A point charge +q is placed at the origin. A second point charge +9q is placed at (d, 0, 0) in Cartesian coordinate system. The point in between them where the electric field vanishes is:

1. (3d/4, 0, 0)
2. (d/4, 0, 0)
3. (4d/3, 0, 0)
4. (d/3, 0, 0)

A small bob of mass 100 mg and charge +10 is connected to an insulating string of length 1 m. It is brought near to an infinitely long non-conducting sheet of charge density ' ' as shown in figure. If string subtends an angle of 45 with the sheet at equilibrium the charge density of sheet will be: (Given, 0 = 8.85 10-12 Fm and acceleration due to gravity, g = 10 ms2) [figure]

1. 1.77 nC/m2
2. 0.885 nC/m2
3. 885 nC/m2
4. 17.7 nC/m2

Consider a circular loop that is uniformly charged and has a radius a 2. Find the position along the positive z-axis of the Cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy plane at the origin :

1. a
2. a/2
3. 0
4. a/ 2

An electric dipole of mass m, charge q, and length l is placed in a uniform electric field E = E0 i. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be :

1. 12 ml2qE0
2. 2 ml2qE0
3. 2 mlqE0
4. 12 2mlqE0

Match List - I with List - II. Choose the correct answer from the options given below :

1. (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
2. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
3. (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
4. (A)-(IV), (B)-(II), (C)-(III), (D)-(I)

A point charge causes an electric flux of -2 104 N m2 C-1 to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is : (Given 0=8.85 10-12 C2 N-1 m-2)

1. 17.7 10-8 C
2. -17.7 10-8 C
3. 15.7 10-8 C
4. -15.7 10-8 C

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density 0. Choose the correct option from the following. [figure]

1. Torque on dipole is zero and net force is directed away from the sheet.
2. Potential energy of dipole is minimum and torque is zero.
3. Potential energy and torque both are maximum.
4. Torque on dipole is zero and net force acts towards the sheet.

A square loop of sides a=1 m is held normally in front of a point charge q=1 C at a distance a2. The flux of the electric field through the shaded region is 5p 1 0 N m2C, where the value of p is . [figure]

A small uncharged conducting sphere is placed in contact with an identical sphere but having 4 10-8 C charge and then removed to a distance such that the force of repulsion between them is 9 10-3 N. The distance between them is (Take 14 0 as 9 109 in SI units)

1. 1 cm
2. 2 cm
3. 4 cm
4. 3 cm

A point particle of charge Q is located at P along the axis of an electric dipole 1 at a distance r as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r. The dipoles are made of opposite charge q separated by a distance 2a. For the charge particle at P not to experience any net force, which of the following correctly describes the situation? [figure]

1. ar 0.5
2. ar 3
3. ar 10
4. ar 20