List of practice Questions

Derive an expression for the magnetic field \(B\), due to a circular coil of \(N\) turns, each of radius \(r\) carrying current \(I\), at a distance \(x\) from the centre along its axis.
Two point charges \(-q\) and \(+q\) are located at points \((-a, 0, 0)\) and \((a, 0, 0)\) respectively. Find the electrostatic potential at point \((x, 0, 0)\) where \(x \gg a\).
Name the electromagnetic waves which are used for (i) detection of fractures in bones
(ii) physiotherapy
(iii) radar systems
Also write their wavelength range.
Define mutual inductance of a pair of coils. Write its SI unit.
A long solenoid of radius \(R\) and length \(L\) has \(n\) turns per unit length. A circular loop of radius \(r(<R)\) is placed inside at the centre of the solenoid such that its axis coincides with the axis of the solenoid. Obtain the mutual inductance of the solenoid and the loop.
Two long straight parallel conductors A and B carrying steady currents \(I_a\) and \(I_b\) in the same direction are separated by a distance \(d\). Deduce the expressions for the force acting on length \(L\) of conductor B due to conductor A and show it in figure. Write the expression for the force acting on length \(L\) of conductor A due to conductor B and show that it follows Newton’s third law.
State Bohr’s second postulate and mention its significance.
Prove that, in Bohr model of hydrogen atom as principal quantum number \(n\) becomes large, the energy levels get closer and closer.
Explain the statement: “Current is a scalar although we represent current with an arrow”.
Find ratio \( \left(\frac{\lambda_a}{\lambda_p}\right) \) of the de Broglie wavelength \( \lambda_a \) and \( \lambda_p \) associated respectively with an alpha particle and a proton,
(i) if they are moving with the same kinetic energy.
(ii) just after they are accelerated through the same potential difference.
A ray of light in air is incident at angle \(i\) on a face of an equilateral glass prism and is refracted through the prism. As \(i\) is varied, it is observed that the ray undergoes minimum deviation, when the \(i\) is three-fourth of the angle of the prism. Calculate the speed of light in the prism.
A heating element using nichrome is connected to a 220 V supply. Initially it draws a current of 2.9 A. After some time, the current attains a steady value of 2.5 A. Find the steady temperature of the heating element if the room temperature is 27 \(^{\circ}\)C. The temperature coefficient of resistance of nichrome is \(1.7 \times 10^{-4}\ ^{\circ}\text{C}^{-1}\).
A 5 cm long pencil is placed along the principal axis of a concave mirror of focal length 20 cm such that its nearest end is at a distance of 25 cm from the mirror. Calculate the length of the image of the pencil.
In a Young’s double-slit experiment, a beam of light consisting of two wavelengths 500 nm and 600 nm is used. The interference fringes are observed at a screen placed 1.8 m away from the plane of slits (slit separation 0.3 mm). Calculate the least distance from the central maximum where the bright fringes due to both the wavelengths coincide.
Consider the following nuclides : \(^{12}_{6}C,\ ^{198}_{80}Hg,\ ^{14}_{6}C,\ ^{197}_{79}Au\). Group them into isotopes and isotones.
How does the size of a nucleus depend on its mass number A? Hence prove that the density of nucleus is a constant, independent of A, for all nuclei.
An electric field \( \vec{E} = E_0 \hat{i} \) exists in a region of space. Draw three equipotential surfaces in the region.
An electromagnetic wave is propagating along x-axis. At any instant, the phase difference between the electric field ($\vec{E}$) and magnetic field ($\vec{B}$) is
In Bohr model, electron transitions from $n=5$ to $n=1$ emit wavelength $\lambda$. What is wavelength for transition $n=5$ to $n=2$?
Assertion (A): On increasing the intensity of incident light of frequency \( v(> v_0) \) on a photosensitive surface, the photocurrent increases. Reason (R): The stopping potential for a photosensitive surface increases with increase of frequency \( v(> v_0) \) of incident light.
Assertion (A): On forward biasing a p-n junction diode, the height of the barrier potential increases. Reason (R): In forward biasing of a p-n junction diode, the direction of the applied voltage is in the same direction as the built-in potential.
Assertion (A): Light added to light can produce darkness. Reason (R): When two coherent light waves interfere, there is darkness at position of destructive interference.
Assertion (A): Two electric heaters of power \( P_1 \) and \( P_2 (> P_1) \) are joined in series across a dc source of voltage \( V \). The power consumed by the combination will be less than that consumed by \( P_1 \) when connected across the same source. Reason (R): The power consumed by an electric device when connected to a dc source of voltage \( V \) is proportional to its resistance.
Write two points of difference between intrinsic and extrinsic semiconductors.
Which of the following materials has positive and small value of magnetic susceptibility?