Which charge configuration produces a uniform electric field ?
a.
Uniformly charged infinite plane
Correct Answer
b.
Point charge
c.
Uniformly charged spherical shell
d.
Uniformly charged infinite line
Step-by-Step AI Explanation
Verified Method
An infinite charged plane produces a uniform electric field where the magnitude is given by $E = \sigma / (2\epsilon_0)$, independent of the distance from the plane. Point charges, spherical shells, and infinite lines all produce non-uniform fields where the magnitude varies with distance $r$ from the source.
Q2mcq1 mark
The blueprint for making ultra durable synthetic material is mimicked from :
a.
Parrot fish
b.
Lotus leaf
c.
Peacock feather
d.
Morpho butterfly
Correct Answer
Step-by-Step AI Explanation
Verified Method
The structural color and the unique lattice structure of the Morpho butterfly's wings, which provide durability and specific optical properties, serve as a model for creating biomimetic ultra-durable synthetic materials.
Q3mcq1 mark
In a transformer, the number of turns in the primary and the secondary are 410 and 1230 respectively. If the current in primary is 6 A, then that in the secondary coil is :
a.
12 A
b.
2 A
Correct Answer
c.
1 A
d.
18 A
Step-by-Step AI Explanation
Verified Method
For an ideal transformer, the relation between current and turns is $N_p / N_s = I_s / I_p$. Given $N_p = 410$, $N_s = 1230$, and $I_p = 6$ A, we have $410 / 1230 = I_s / 6$, which simplifies to $1/3 = I_s / 6$. Therefore, $I_s = 6 / 3 = 2$ A.
Q4mcq1 mark
Which of the following is false for electromagnetic waves ?
a.
longitudinal
Correct Answer
b.
transverse
c.
produced by accelerating charges
d.
non-mechanical waves
Step-by-Step AI Explanation
Verified Method
Electromagnetic waves are transverse in nature, meaning the electric and magnetic field vectors oscillate perpendicular to the direction of propagation. They are produced by accelerating charges and are non-mechanical (do not require a medium). They are not longitudinal.
Q5mcq1 mark
If the nuclear radius of $^{27}\text{Al}$ is 3.6 fermi, the approximate nuclear radius of $^{64}\text{Cu}$ in fermi is :
a.
4.8
Correct Answer
b.
2.4
c.
3.6
d.
1.2
Step-by-Step AI Explanation
Verified Method
The nuclear radius is given by $R = R_0 A^{1/3}$. Thus, $R_1 / R_2 = (A_1 / A_2)^{1/3}$. For $^{27}\text{Al}$ ($A=27$), $R_1 = 3.6$. For $^{64}\text{Cu}$ ($A=64$), $R_2 / 3.6 = (64/27)^{1/3} = 4/3$. Thus, $R_2 = 3.6 \times (4/3) = 4.8$ fermi.
Q6mcq1 mark
The unit of electric flux is :
a.
Nm$^{-1}$C$^{2}$
b.
Nm$^{-2}$C$^{-1}$
c.
Nm$^{2}$C$^{-1}$
Correct Answer
d.
N$^{2}$mC$^{-1}$
Step-by-Step AI Explanation
Verified Method
Electric flux is defined as $\Phi_E = E \cdot A$. The unit of $E$ is N/C (or V/m) and the unit of area $A$ is m$^2$. Thus, the unit of electric flux is $(\text{N/C}) \times \text{m}^2 = \text{Nm}^2\text{C}^{-1}$.
Q7mcq1 mark
In an oscillating LC circuit, the maximum charge on the capacitor is Q. The charge on the capacitor when the energy is stored equally between the electric and magnetic fields is :
a.
Q/2
b.
Q/\sqrt{2}
Correct Answer
c.
Q
d.
Q/3
Step-by-Step AI Explanation
Verified Method
Total energy $U = Q^2 / (2C)$. When energy is shared equally, the energy in the electric field is $U_E = U / 2 = Q^2 / (4C)$. Since $U_E = q^2 / (2C)$, we equate $q^2 / (2C) = Q^2 / (4C)$, which gives $q^2 = Q^2 / 2$, so $q = Q / \sqrt{2}$.
Q8mcq1 mark
The ratio of magnetic length and geometrical length is :
a.
0.833
Correct Answer
b.
0.633
c.
0.933
d.
0.733
Step-by-Step AI Explanation
Verified Method
The magnetic length of a bar magnet is approximately $0.833$ (or $5/6$) of its geometrical length due to the fact that the poles are located slightly inside the ends of the magnet.
Q9mcq1 mark
The Zener diode is primarily used as :
a.
Oscillator
b.
Rectifier
c.
Voltage regulator
Correct Answer
d.
Amplifier
Step-by-Step AI Explanation
Verified Method
A Zener diode is specifically designed to operate in the reverse breakdown region. When the reverse voltage across it reaches the Zener voltage, the voltage remains constant despite variations in the input voltage or load current, making it an ideal voltage regulator. Oscillators, rectifiers, and amplifiers typically use different circuit configurations or diode types (like PN junction diodes for rectification).
Q10mcq1 mark
If the Velocity and Wavelength of light in air is $V_a$ and $\lambda_a$ and that in water is $V_w$ and $\lambda_w$, then the refractive index of water is :
a.
$\lambda_w/\lambda_a$
b.
V_w/V_a
c.
$(V_a \lambda_a) / (V_w \lambda_w)$
d.
V_a/V_w
Correct Answer
Step-by-Step AI Explanation
Verified Method
The refractive index of a medium with respect to air is defined as the ratio of the speed of light in air to the speed of light in that medium. Therefore, $\mu = V_a / V_w$. Since the frequency ($f$) of light remains constant when it travels from one medium to another, and using the relation $V = f \lambda$, we have $V_a = f \lambda_a$ and $V_w = f \lambda_w$. Substituting these gives $\mu = (f \lambda_a) / (f \lambda_w) = \lambda_a / \lambda_w$. Option (d) is the correct expression for the refractive index in terms of velocity. Option (a) is the inverse of the refractive index. Options (b) and (c) are incorrect based on the definition of refractive index.
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A particle having mass m and charge q accelerated through a potential difference V. Find the force experienced when it is kept under perpendicular magnetic field $\vec{B}$.
a.
$\frac{3}{2} q B \sqrt{\frac{2V}{m}}$
b.
$q B \sqrt{\frac{2qV}{m}}$
c.
$\frac{3}{3} q B \sqrt{\frac{2qV}{m}}$
d.
$\frac{3}{2} q B \sqrt{\frac{qV}{2m}}$
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In a Young’s double slit experiment, the slit separation is doubled. To maintain the same fringe spacing on the screen, the screen-to-slit distance D must be changed to :
a.
2 D
b.
2 D (Note: typo in source, duplicate 2D)
c.
D/2
d.
D/2 (Note: typo in source, duplicate D/2)
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Dielectric strength of air is 4×10$^{6}$ Vm$^{-1}$. Suppose the radius of a hollow sphere in the Van de Graaff generator is R=0.4 m, calculate the maximum potential difference created by this Van de Graaff generator.
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The repulsive force between two magnetic poles in air is 9×10$^{-3}$ N. If the two poles are equal in strength and are separated by a distance of 10 cm, calculate the pole strength of each pole.
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$^{92}\text{U}^{235}$ nucleus emits 2$\alpha$ particles, 3$\beta$ particles and 2$\gamma$ particles. What is the resulting atomic number and mass number ?
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(a) Deduce the relation for the magnetic field at a point due to an infinitely long straight conductor carrying current. OR (b) Obtain the law of radioactivity.
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(a) Calculate the electric field due to a dipole on its axial line. OR (b) What is Frequency Modulation ? List out the advantages and limitations of frequency modulation.
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(a) (i) Derive an expression for de Broglie wavelength of electrons. (ii) Calculate the momentum of an electron with kinetic energy 2 eV. OR (b) Write down Maxwell
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(a)Explain about Astronomical telescope and obtain the equation for the magnification. OR (b)(i)Explain the equivalent resistance of a series resistor network. (ii)A Copper wire of cross-sectional area 0.5 $mm^2$ carries a current of 0.2 A. If the free electron density of copper is $8.4 \times 10^{28} m^{-3}$ then compute the drift velocity of free electrons.
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(a) Explain about Astronomical telescope and obtain the equation for the magnification. OR (b) (i) Explain the equivalent resistance of a series resistor network. (ii) A Copper wire of cross-sectional area 0.5 mm$^{2}$ carries a current of ...
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A Copper wire of cross-sectional area 0.5 mm$^{2}$ carries a current of 0.2 A. If the free electron density of copper is $8.4 \times 10^{28}$ m$^{-3}$ then compute the drift velocity of free electrons.
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