The electric field associated with an electromagnetic wave in vaccum is given by E = i 40 cos (kz − 6 x 10⁸ t), where E, Z and t are in volt m^-1, metre and second respectively. The value of wave vector (k) is

• 2 m^-1

• 0.5 m^-1

• 6 m^-1

• 3 m^-1

32.

In the shown figure, what is the potential difference between the points A and B and between B and C respectively in steady state ? 

   

• V_AB = V_BC = 100 V

• V_AB = 75 V , V_BC = 25 V

• V_AB = 25 V , V_BC = 75 V

• V_AB = V_BC = 50 V

A resistance of 4 Ω and a wire of length 5 m and resistance 5 Ω are joined in series and connected to a cell of emf 10 V and internal resistance of 1 Ω. A parallel combination of two identical cells in balanced across 3 m of the wire. The emf E of each cell is

• 1.5 V

• 3.0 V

• 0.67 V

• 1.33 V

An L-C-R series circuit with 100 Ω resistance is connected to an AC source of 200 V and angular frequency 300 rad s^-1 . When only the capacitance is removed, the current lags behind the voltage by 60°. When only the inductance is removed, the current leads the voltage by 60°. The average power dissipated in this L-C-R circuit is

• 0

• 400 W

• 200 W

• 800 W

Two concentric conducting spherical shells A and B having radii r_A and r_B (r_B > rA) are charged to Q_A and -Q_B $\left(\left|{\mathrm{Q}}_{\mathrm{B}}\right| > \left|{\mathrm{Q}}_{\mathrm{A}}\right|\right)$ . The electric field along a line passing through the centre is

• $\left|{\mathrm{Q}}_{\mathrm{B}}\right| > \left|{\mathrm{Q}}_{\mathrm{A}}\right|$

• 

• 

• 

Electrons with de-Broglie wavelength λ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is

• ${\mathrm{\lambda }}_0 = \frac{2{\mathrm{mc\lambda }}^2}{\mathrm{h}}$

• ${\mathrm{\lambda }}_0 = \frac{2\mathrm{h}}{\mathrm{mc}}$

• ${\mathrm{\lambda }}_0 = \frac{2{\mathrm{m}}^2{\mathrm{c}}^2{\mathrm{\lambda }}^3}{{\mathrm{h}}^2}$

• ${\mathrm{\lambda }}_0 = \mathrm{\lambda }$

The figure illustrates how the flux density B inside a sample of demagnetised ferromagnetic material varies with the magnetic flux density B₀ , in which the sample is kept. For the sample to be suitable for making a permanent magnet, then which statement is true for this?

• OQ should be large, OR should be small

• both OQ and OR should be large

• OQ should be small and OR should be large

• both OQ and OR should be small

Two straight infinitely long current carrying wires are kept along Z-axis at the co-ordinates (0, a, O) and (0, -a, 0) respectively, as shown in figure. The current in each of the wire is equal and along negative Z-axis (into the plane of the paper).

The variation of magnetic field on the X-axis will be approximately

The co-ordinates of centre of mass of the uniform lamina shown in figure, is if smal disc of radius $\frac{\mathrm{a}}{2}$  is cut from disc of radius a

• $\left(\frac{\mathrm{a}}{6} , \frac{\mathrm{a}}{6}\right)$

• $\left(\frac{\mathrm{a}}{6} , 0\right)$

• $\left(\mathrm{o} , \frac{-\mathrm{a}}{6}\right)$

• $\left(\frac{-\mathrm{a}}{6} , 0\right)$

A toroid having 200 turns carries a current of 1A. The average radius of the toroid is 10 cm. The magnetic field at any point in the open space inside the toroid is

• 4 × 10^-3 T

• 0.5 × 10^-3 T

• 0

• 3 × 10^-3 T