List of top Physics Questions on Electric Fields and Gauss' Law

Two point charges \( q_1 = 16 \, \mu C \) and \( q_2 = 1 \, \mu C \) are placed at points \( \vec{r}_1 = (3 \, \text{m}) \hat{i}\) and \( \vec{r}_2 = (4 \, \text{m}) \hat{j} \). Find the net electric field \( \vec{E} \) at point \( \vec{r} = (3 \, \text{m}) \hat{i} + (4 \, \text{m}) \hat{j} \).

Obtain an expression for the electric field \( \vec{E} \) due to a dipole of dipole moment \( \vec{p} \) at a point on its equatorial plane and specify its direction.
Hence, find the value of electric field:

  1. at the centre of the dipole (\( r = 0 \))
  2. at a point \( r \gg a \), where \( 2a \) is the length of the dipole.
Current I (= 1 A) is passing through a copper rod (n = \(8.5 \times 10^{28} \, \text{m}^{-3}\)) of varying cross-sections as shown in the figure. The areas of cross-section at points A and B along its length are \(1.0 \times 10^{-7} \, \text{m}^2\) and \(2.0 \times 10^{-7} \, \text{m}^2\) respectively. Calculate:
Current I (= 1 A) is passing through a copper rod
(I) the ratio of electric fields at points A and B.
(II) the drift velocity of free electrons at point B.
An electric field \( \vec{E} = (10x + 5) \hat{i} \, \text{N/C} \) exists in a region in which a cube of side \( L \) is kept as shown in the figure. Here \( x \) and \( L \) are in metres. Calculate the net flux through the cube.
An electric field E⃗ = (10x + 5)ˆi N/C
An electron of charge e and mass m is kept in a uniform electric field E, then the acceleration of the electron will be
An electric dipole consists of two opposite charges each of magnitude 1 µC, separated by 2 cm. The dipole is placed in an external electric field of \( 10^5 \, \text{N/C} \). Calculate the:
(i) maximum torque experienced by the dipole
(ii) work done by the external field to turn the dipole through 180°
State the formula giving relation between electric field intensity and potential gradient.