Science (English Medium) Class 12 - CBSE Important Questions

An electric dipole of length 1 cm, which placed with its axis making an angle of 60° with uniform electric field, experience a torque of \[6\sqrt{3} Nm\] . Calculate the potential energy of the dipole if it has charge ±2 nC.

Given a uniform electric filed \[\vec{E} = 4 \times {10}^3 \ \hat{i} N/C\]. Find the flux of this field through a square of 5 cm on a side whose plane is parallel to the Y-Z plane. What would be the flux through the same square if the plane makes a 30° angle with the x-axis?

A hollow cylindrical box of length 0.5 m and area of cross-section 25 cm² is placed in a three dimensional coordinate system as shown in the figure. The electric field in the region is given by `vecE = 20 xhati`  where E is NC­⁻¹ and x is in metres. Find

(i) Net flux through the cylinder.

(ii) Charge enclosed by the cylinder.

Two charges of magnitudes −2Q and +Q are located at points (a, 0) and (4a, 0) respectively. What is the electric flux due to these charges through a sphere of radius ‘3a’ with its centre at the origin?

Two charges of magnitudes −3Q and + 2Q are located at points (a, 0) and (4a, 0) respectively. What is the electric flux due to these charges through a sphere of radius ‘5a’ with its centre at the origin?

Two charges of magnitudes +4Q and − Q are located at points (a, 0) and (− 3a, 0) respectively. What is the electric flux due to these charges through a sphere of radius ‘2a’ with its centre at the origin?

Define electric dipole moment. 

A thin straight infinitely long conducting wire having charge density λ is enclosed by a cylindrical surface of radius r and length l, its axis coinciding with the length of the wire. Find the expression for the electric flux through the surface of the cylinder.

Figure shows three point charges +2q, −q and + 3q. Two charges + 2q and −q are enclosed within a surface ‘S’. What is the electric flux due to this configuration through the surface ‘S’?

In which orientation, a dipole placed in a uniform electric field is in (i) stable, (ii) unstable equilibrium?

A thin conducting spherical shell of radius R has charge Q spread uniformly over its surface. Using Gauss’s law, derive an expression for an electric field at a point outside the shell.

Draw a graph of electric field E(r) with distance r from the centre of the shell for 0 ≤ r ≤ ∞.

State Gauss’s law for magnetism. Explain its significance. 

Answer the following question.
State Gauss's law for magnetism. Explain its significance.

Deduce the expression for the torque `vec"τ"` acting on a planar loop of area `vec"A"` acting on a planar loop of area `vec"B"`. If the loop is free to rotate, what would be its orientation in stable equilibrium?

State Gauss's law in electrostatics. Show, with the help of a suitable example along with the figure, that the outward flux due to a point charge 'q'. in vacuum within a closed surface, is independent of its size or shape and is given by `q/ε_0`

State Gauss’s law on electrostatics and drive expression for the electric field due to a long straight thin uniformly charged wire (linear charge density λ) at a point lying at a distance r from the wire.

An electric dipole is placed at an angle of 30° with an electric field intensity of 2 × 10⁵ N/C. It experiences a torque equal to 4 Nm. The charge on the dipole, if the dipole length is 2 cm, is ______.

The electric potential V as a function of distance X is shown in the figure.

The graph of the magnitude of electric field intensity E as a function of X is ______.

Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.7 × 10^–22 C/m². What is electric field intensity E:

1. in the outer region of the first plate, and
2. between the plates?