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The electric field of an electromagnetic wave in free space is given by $\vec{E} = 10 \cos(10^7 t + kx) \hat{j}$ V/m, where $t$ and $x$ are in seconds and meters respectively. It can be inferred that: (1) The wavelength $\lambda$ is $188.4 \text{ m}$. (2) The wave number $k$ is $0.33 \text{ rad/m}$. (3) The wave amplitude is $10 \text{ V/m}$. (4) The wave is propagating along $+x$ direction. Which one of the following pairs of statements is correct?
If the unit of length and force be increased four times, then the unit of energy is:
Which of the following pairs of physical quantities has the same dimensions?
A, B and C are three points in a uniform electric field. The electric potential is:
The electric potential at a point in free space due to a charge $Q$ coulomb is $Q \times 10^{11}$ V. The electric field at that point is:
Four point charges -Q, -q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero, is
If potential in a region is expressed as $V(x,y,z) = 6xy - y + 2yz$, the electric field at point $(1, 1, 0)$ is:
Two spheres of radius $a$ and $b$ respectively are charged and joined by a wire. The ratio of the electric field at the surface of the spheres is:
The force $F$ on a sphere of radius ‘$a$’ moving in a medium with velocity ‘$v$’ is given by $F = 6\pi\eta av$. The dimensions of $\eta$ are:
Which of the following represents a volt?
Two metal spheres, one of radius $R$ and the other of radius $2R$ respectively have the same surface charge density $\sigma$. They are brought in contact and separated. What will be the new surface charge densities on them?
The units of angular momentum are:
The effective capacitances of two capacitors are $3 \text{ \mu F}$ and $16 \text{ \mu F}$, when they are connected in series and parallel respectively. The capacitance of two capacitors are:
The equation of a wave is given by $Y = A \sin \omega (\frac{x}{v} - k)$ where $\omega$ is the angular velocity, $x$ is length and $v$ is the linear velocity. The dimension of $k$ is:
Dimensions of resistance in an electrical circuit, in terms of dimension of mass $M$, length $L$, time $T$, and current $I$, would be:
The value of Planck's constant is
The pair having the same dimensions is:
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The potential (V) at any axial point, at 2 m distance (r) from the centre of the dipole of dipole moment vector P of magnitude, $4\times10^{-6}$ C m, is $\pm 9\times10^3$ V. (Take $1/4\pi\varepsilon_0 = 9\times10^9$ SI units) Reason (R): $V = \pm \frac{2P}{4\pi\varepsilon_0 r^2}$, where r is the distance of any axial point situated at 2 m from the centre of the dipole. In the light of the above statements, choose the correct answer from the options given below:
The main scale of a vernier calliper has $n$ divisions/cm. $n$ divisions of the vernier scale coincide with $(n-1)$ divisions of the main scale. The least count of the vernier calliper is:
A series combination of n₁ capacitors, each of value C₁, is charged by a source of potential difference 4V. When another parallel combination of n₂ capacitors, each of value C₂, is charged by a source of potential difference V, it has the same (total) energy stored in it as the first combination has. The value of C₂ in terms of C₁ is: