Time Varying Fields · Electromagnetic Fields · GATE EE

In cylindrical coordinate system, the potential produced by a uniform ring charge is given $$\phi=f\left(r,\;z\right)$$, where f is a continuous function of r and z. Let $$\overrightarrow E$$ be the resulting electric field. Then the magnitude of $$\nabla\times\overrightarrow E$$

Consider a one-turn rectangular loop of wire placed in a uniform magnetic field as shown in the figure. The plane of the loop is perpendicular to the field lines. The resistance of the loop is 0.4 Ω, and its inductance is negligible. The magnetic flux density (in Tesla) is a function of time, and is given by B(t) = 0.25 sinωt, where ω = 2𝜋×50 radian/second. The power absorbed (in Watt) by the loop from the magnetic field is ________.

A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown in the figure. The value of μ0 is $$4\mathrm\pi\times10^{-7}$$ in SI unit. If a uniform magnetic field intensity $$\overrightarrow H=10^7\;\widehat z\;A/m$$ is applied, then the peak value of the induced voltage, V_turn ( in Volts), is _________.

The concept of an electrically short, medium, and long line is primarily based on the

An electromagnetic field is radiated from

The laws of electromagnetic induction (Faraday's and Lenz's law) are summarized in the following equation

A monochromatic plane electromagnetic wave travels in vacuum in the position $$x$$ direction ($$x, y, z$$ system of coordinates). The electric and magnetic fields can be expressed as

Consider the following statements with reference to the equation $$\nabla.\overrightarrow J=-\frac{\partial\rho}{\partial t}$$

1. This is a point from the continuity equation
2. Divergence of current density is equal to the decrease of charge per unit volume per unit time at every point.
3. This is Maxwell's divergence equation
4. This represents the conservation of charge.

Select the correct answer.

The velocity of propagation of electromagnetic wave 'n' an underground cable with relative permittivity of 3 will be ________m/sec

A square coil of $$10$$ turns and $$10$$ $$cm$$ side is moved through a steady magnetic field of $$1$$ $$Wb/{m^2}$$ at a constant velocity of $$2$$ $$m/sec$$ with its plane perpendicular to the field as shown in Fig. Plot the variation of induced $$e.m.f$$ as the coil moves along the field.

Match the following List-$${\rm I}$$ with List-$${\rm II}$$

List $$-$$ $${\rm I}$$
$$(a)$$ Line charge
$$(b)$$ Magnetic Flux Density
$$(c)$$ Displacement current
$$(d)$$ Power flow

List $$-$$ $${\rm II}$$
$$(P)$$ Maxwell's
$$(Q)$$ Poynting vector
$$(R)$$ Transmission line conductors
$$(S)$$ Biot-Savart's law
$$(T)$$Gauss's law
$$(U)$$ Faraday's law