List of practice Questions

A circular coil of \(100\) turns and radius \[ \left(\frac{10}{\pi}\right)\text{ cm} \] carrying current \(5.0\) A is suspended vertically in a uniform horizontal magnetic field of \(2.0\) T. The field makes an angle \(30^\circ\) with the normal to the coil. Calculate:
(I) the magnetic dipole moment of the coil, and
(II) the magnitude of the counter torque required to prevent the coil from turning.

Derive an expression for the force \(\vec F\) acting on a conductor of length \(L\) and area of cross-section \(A\) carrying current \(I\) and placed in a magnetic field \(\vec B\).

A part of a wire carrying \(2.0\) A current and bent at \(90^\circ\) at two points is placed in a region of uniform magnetic field \[ \vec B=-0.50\,\hat k\,T. \]

Calculate the magnitude of the net force acting on the wire.

A parallel beam of monochromatic light falls normally on a single slit of width \(a\) and a diffraction pattern is observed on a screen placed at distance \(D\) from the slit. Explain:
(I) the formation of maxima and minima in the diffraction pattern, and
(II) why the maxima go on becoming weaker and weaker with increasing order \(n\).

Write any two points of difference between interference pattern due to double-slit and diffraction pattern due to single-slit.

With the help of a ray diagram, describe the construction and working of a compound microscope.

(I) The real image of an object placed between \(f\) and \(2f\) from a convex lens can be seen on a screen placed at the image location. If the screen is removed, is the image still there? Explain.
(II) Plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances? Explain.

Derive the condition for which a Wheatstone Bridge is balanced.

Determine the current in \(3\,\Omega\) branch of a Wheatstone Bridge in the circuit shown in the figure.

Consider a cylindrical conductor of length \(l\) and area of cross-section \(A\). Current \(I\) is maintained in the conductor and electrons drift with velocity \(v_d\). Show that the conductivity \(\sigma\) of the material of the conductor is given by \[ \sigma=\frac{ne^2\tau}{m}. \]

The resistance of a metal wire at \(20^\circ\text{C}\) is \(1.05\,\Omega\) and at \(100^\circ\text{C}\) is \(1.38\,\Omega\). Determine the temperature coefficient of resistivity of this metal.

A rectangular loop of sides \(a\) and \(b\) carrying current \(I\) is placed in a magnetic field \(\vec B\) such that its area vector \(\vec A\) makes an angle \(\theta\) with \(\vec B\). With the help of a suitable diagram, show that the torque \(\vec \tau\) acting on the loop is given by \[ \vec \tau=\vec m\times \vec B, \] where \[ \vec m=I\vec A \] is the magnetic dipole moment of the loop.

Photoemission of electrons occurs from a metal \((\phi_0=1.96\,\text{eV})\) when light of frequency \(6.4\times10^{14}\,\text{Hz}\) is incident on it. Calculate the stopping potential.

Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

Write any two features of nuclear forces.

If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

If Bohr's quantization postulate \(\left(L=\dfrac{nh}{2\pi}\right)\) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

Photoemission of electrons occurs from a metal \((\phi_0=1.96\,\text{eV})\) when light of frequency \(6.4\times10^{14}\,\text{Hz}\) is incident on it. Calculate: Energy of a photon in the incident light.

Photoemission of electrons occurs from a metal \((\phi_0=1.96\,\text{eV})\) when light of frequency \(6.4\times10^{14}\,\text{Hz}\) is incident on it. Calculate the maximum kinetic energy of the emitted electrons.

Suppose a pure Si crystal has \(5\times10^{28}\) atoms per \(\text{m}^3\). It is doped with \(5\times10^{22}\) atoms per \(\text{m}^3\) of Arsenic. Calculate the majority and minority carrier concentration in the doped silicon. Given: \[ n_i=1.5\times10^{16}\,\text{m}^{-3} \]

Two parallel plate capacitors X and Y are connected in series to a 6 V battery. They have the same plate area and same plate separation but capacitor X has air between its plates, whereas capacitor Y contains a material of dielectric constant 4. Calculate the capacitances of X and Y, if the equivalent capacitance of the combination of X and Y is \(4\,\mu\text{F}\).

Calculate the potential difference across the plates of capacitors X and Y.

Write the expression for the magnetic field due to a current element in vector form. Consider a \(1\,\text{cm}\) segment of a wire, centered at the origin, carrying a current of \(10\,\text{A}\) in positive \(x\)-direction. Calculate the magnetic field \(\vec{B}\) at a point \((1\,\text{m},1\,\text{m},0)\).

A long solenoid of length \(L\) and radius \(r_1\) having \(N_1\) turns is surrounded symmetrically by a coil of radius \(r_2\,(>r_1)\) having \(N_2\) turns \((N_2 \ll N_1)\) around its mid-point. Derive an expression for the mutual inductance of the solenoid and the coil. Is \(M_{12}=M_{21}\) valid in this case?