Electric Charges and Fields

The electric field in a certain region is acting radially outward and is given by E = Ar. A charge contained in a sphere of radius 'a' centred at the origin of the field will be given by

In a coil of resistance 10Ω, the induced current developed by changing magnetic flux through it is shown in the figure as a function of time. The magnitude of change in flux through the coil in weber is 

• 8

• 2

• 6

• 6

What is the flux through a cube of side a if a point charge of q is a one of its corner?

Two thin dielectric slabs of dielectric constants K₁ and K₂ (K₁ < K₂) 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 plate P is correctly shown by:

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

• zero and 

• 

• 

• 

In a region, the potential is represented by V (x,y,z) = 6x - 8 xy - 8y + 6yz, where V is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1,1,1) is,

• 6√5 N

• 30 N

• 24 N

• 24 N

A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will 

• be reduced to half

• remain the same

• be doubled

• be doubled

A beam of cathode rays is subjected to crossed Electric (E)  and magnetic field (B). The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by  

(Where V is the potential difference between cathode and anode)

• B²/2VE²

• 2VB²/E²

• 2VE²/B²

• 2VE²/B²

The electric field at a distance 3R/2 from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance R/2 from the centre of the sphere is

• zero

• E

• E/2

• E/2

The electric field of an electromagnetic wave in free space is given by , where t and x are in seconds and meters respectively. It can be inferred that

1) the wavelength λ is 188.4 m.
2)The wave number k is 0.33 rad/m.
3)The wave amplitude is 10 V /m.
4)The wave is propagating along +x direction

• (3) and (4)

• (1) and (2) 

• (2) and (3)

• (2) and (3)