Intensity of an electric field (E) depends on distance r, due to a dipole, is related as ?

The electric potential V at any point (x, y, z), all in meters in space is given by V = 4x2 volt. The electric field at the point (1, 0, 2) in volt/ meter is ?

The formation of a dipole is due to two equal and dissimilar point charges placed at a ?

A spherical conductor of radius 10 cm has a charge of 3.2 × 10−7C distributed uniformly. What is the magnitude of electric field at a point 15 cm from the centre of the sphere ?

Two parallel infinite line charges with linear charge densities +λC/m and −λC/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges ?

A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at ?

An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is ?

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E. Due to the force qE , its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively ?

An electric dipole of dipole moment p is aligned parallel to a uniform electric field E. The energy required to rotate the dipole by 90◦ is ?

An electric dipole of moment p ′ is placed in an electric field of intensity ’ E ’. The dipole acquires a position such that the axis of the dipole makes an angle θ with the direction of the field. Assuming that the potential energy of the dipole to be zero when = 90◦ , the torque and the potential energy of the dipole will respectively be: ?

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 ?

The mean free path of electrons in a metal is 4×10−8 m. The electric field which can give on an average 2eV energy to an electron in the metal will be in units of V/m ?

A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring is ?

Three point charges +q, −q and +q are placed at points (x = 0, y = a, z = 0),(x = 0, y = 0, z = 0) and (x = a, y = 0, z = 0) respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are ?

The electric intensity due to a dipole of length 10 cm and having a charge of 500μC, at a point on the axis at a distance 20 cm from one of the charges in air, is ?

If a dipole of dipole moment p is placed in a uniform electric field E, then torque acting on it is given by ?

If a dipole of dipole moment \( \vec{p} \) is placed in a uniform electric field \( \vec{E} \), then the torque acting on it is given by ?

<p>(a) \( \vec{\tau} = \vec{p} \cdot \vec{E} \)</p>

<p>(b) \( \vec{\tau} = \vec{p} \times \vec{E} \)</p>

<p>(c) \( \vec{\tau} = \vec{p} + \vec{E} \)</p>

<p>(d) \( \vec{\tau} = \vec{p} - \vec{E} \)</p>

Answer :  <p>(b) \( \vec{\tau} = \vec{p} \times \vec{E} \)</p>

A semi-circular arc of radius ’ a ’ is charged uniformly and the charge per unit length is λ. The electric field at the centre of this arc is ?

A hollow insulated conduction sphere is given a positive charge of 10μC. What will be the electric field at the centre of the sphere if its radius is 2 metres ?

A point Q lies on the perpendicular bisector of an electrical dipole of dipole moment p. If the distance of Q from the dipole is r (much larger than the size of the dipole), then the electric field at Q is proportional to ?

From a point charge, there is a fixed point A. At A, there is an electric field of 500 V/m and potential difference of 3000 V. Distance between point charge and A will be ?