Symmetry in Laws

Q. Which of the following is not a Maxwell's equation?

1. $\oint \overrightarrow{B}.d\overrightarrow{A}=0$
2. $\oint \overrightarrow{E}.d\overrightarrow{A}=\frac{q_{\text{in}}}{{ϵ}_0}$
3. $\oint \overrightarrow{E}.d\overrightarrow{l}=-\frac{d{\varphi }_B}{dt}$
4. $\oint \overrightarrow{E}.d\overrightarrow{l}=V$

Q. (iv)$\oint \overrightarrow{B}.\overrightarrow{d}s={\mu }_0{\epsilon }_0\frac{d}{dt}\oint \overrightarrow{E}.\overrightarrow{d}s$

1. (i) and (iv)
2. (ii) only
3. (iii) only
4. none of these

Q. A ball of radius R=50 cm is located in a non-magnetic medium with permitivity k = 4.0. In that medium a plane electromagnetic wave propagates, the strength amplitude of whose electric component is equal to $E_m=200V/m$. The amount of energy that reaches the ball during a time interval of $t=1.0\min$ is (in kJ) ?

Q. (iv)$\oint \overrightarrow{B}.\overrightarrow{d}s={\mu }_0{\epsilon }_0\frac{d}{dt}\oint \overrightarrow{E}.\overrightarrow{d}s$

1. (i) only
2. (ii) only
3. (iii) only
4. (iv) only

Q. Relative permeability and relative permitivity of a medium are respectively $4$ and $9$. If the magnetic induction field of the electromagnetic wave travelling in the medium is $4.2\times {10}^{-8}T$, then the magnitude of its electric field is

1. $4.2V{m}^{-1}$
2. $4.2\times {10}^{-8}V{m}^{-1}$
3. $2.1\times {10}^{-8}V{m}^{-1}$
4. $2.1V{m}^{-1}$

Q. An electron accelerated through a potential of $10,000V$ from rest has a de-Broglie wave length ${}^{\prime }{\lambda }^{\prime }$. What should be the accelerating potential so that the wave length is doubled?

1. $2,500V$
2. $40,000V$
3. $20,000V$
4. $5,000V$

Q. In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacemnt is $0.17s$. The
frequency of the wave is

1. $1.47Hz$
2. $0.36Hz$
3. $0.73Hz$
4. $2.94Hz$

Q. A toroidal coil of rectangular crossection has an inner radius a, outer radius b, height h and total number of turns N. Current in the toroid is $i$, and say $r$ is distance of a point from the center of toroid.

1. Magnetic field at the point decreases with r for 0 < r < a
2. Magnetic field at the point increases with r for a < r < b
3. Magnetic field is zero for r > b
4. Self inductance of toroid is $\frac{{\mu }_0{N}^{2}h}{2\pi }ln\left(\frac{b}{a}\right)$

Q. A ball of radius R=50 cm is located in a non-magnetic medium with permitivity k = 4.0. In that medium a plane electromagnetic wave propagates, the strength amplitude of whose electric component is equal to $E_m=200V/m$. The amount of energy that reaches the ball during a time interval of $t=1.0\min$ is (in kJ) ?