CBSE Class 12 Physics — Electric Charges and Fields

(a) Using Gauss's law, deduce an expression for electric field at a point due to a uniformly charged infinite plane thin sheet. (b) Two large thin plane sheets, each having surface charge density σ, are held close and parallel to each other in air. What is the net electric field at a point (i) inside and (ii) outside, the sheets? OR (a) Obtain the condition of balance of a Wheatstone bridge. (b) Find net resistance of the network of resistors connected between A and B, as shown in figure.

Figure shows a narrow beam of electrons entering with a velocity of $3 \times 10^7$ m/s, symmetrically through the space between two parallel horizontal plates $P_1 P_1'$ and $P_2 P_2'$ kept 2 cm apart. If each plate is 3 cm long, calculate the potential difference V applied between the plates so that the beam just strikes the end $P_2'$.

(a) An electric dipole consists of two point charges q and $-q$ separated by a distance $2a$. Derive an expression for the electric field E due to this dipole at a point distant r from the centre of the dipole on the equatorial plane. Write the expression for the electric field at a far off point, i.e. $r \gg a$. (b) A dipole is placed in x-y plane such that charges q and $-q$ are located at $x = a$ and $x = b$ respectively. There exists an electric field $E = 2\hat{i}\text{ N/C}$ in the region. Calculate the force F and torque τ experienced by the dipole. OR (a) Two cells of emf $E_1$ and $E_2$ with internal resistances $r_1$ and $r_2$ respectively, are connected in parallel by connecting their positive terminals together and negative terminals together. Deduce an expression for equivalent emf and equivalent internal resistance of the combination. (b) A parallel combination, as stated in (a) above, of two cells of emfs $E$ and $3E$ and internal resistances R each is connected across a resistance $2R$. Find the current that flows through resistance $2R$.