Consider three quantities x= E B , y= 1 _0 _0 and z=1 CR . Here, … - Vidyadip

MCQ

Consider three quantities $\text{x}=\frac{\text{E}}{\text{B}},\ \text{y}=\sqrt{\frac{1}{\mu_0\in_0}}$ and $\text{z}=\frac{1}{\text{CR}}.$ Here, l is the length of a wire, C is a capacitance and R is a resistance. All other symbols have standard meanings.

A
x, y have the same dimensions.
B
y, z have the same dimensions.
C
z, x have the same dimensions.
✓
All of the above.

✓

Answer

Correct option: D.

All of the above.

Explanation:
Lorentz Force:
$\text{qvB}=\text{qE}$
⇒ Dimensions of $\text{x}=[\text{v}]=\Big[\frac{\text{E}}{\text{B}}\Big]=\big[\text{LT}^{-1}\big]$
$\text{y}=\frac{1}{\sqrt{\mu_0\in_0}}=\sqrt{\frac{4\pi}{\mu_0}\times\frac{1}{4\pi\in_0}}=\sqrt{\frac{9\times10^9}{10^{-7}}}=3\times10^8=\text{c}$
⇒ Dimensions of $\text{y}=[\text{c}]=\big[\text{LT}^{-1}\big]$
Time constant of RC circuit = RC so dimensionally [RC] = [T]
$\Rightarrow\text{z}=\Big[\frac{\text{l}}{\text{RC}}\Rightarrow[\text{z}]=[\text{LT}^{-1}]$
Therefore, x, y and z have the same dimensions.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Moving Charges and Magnetism→Moving Charges and Magnetism — all question types→Physics STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The unit of magnetic flux is

In Young's double slit experiment, monochromatic light of wavelength $5000$ $A$ is used. The slits are $1.0 \mathrm{~mm}$ apart and screen is placed at $1.0 \mathrm{~m}$ away from slits. The distance from the centre of the screen where intensity becomes half of the maximum intensity for the first time is___________ $10^{-6} \mathrm{~m}$.

In the figure four plate characteristics of a triode at different grid voltage are shown. The difference between successive grid voltage is $1 V.$ Which curve will have maximum grid voltage and what is its value?

The binding energy of the innermost electron in tungsten is 40 keV. To produce characteristic X-rays using a tungsten target in an X-rays tube the potential difference V between the cathode and the anti-cathode should be

Glass has refractive index $\mu $ with respect to air and the critical angle for a ray of light going from glass to air is $\theta$. If a ray of light is incident from air on the glass with angle of incidence $\theta$, the corresponding angle of refraction is

There are certain types of stars called visible stars which undergo periodic change in their light output. If such a star quadruple it's light output, how much does it's magnitude change

A capacitor of capacitance 5$\mu F$ is connected as shown in the figure. The internal resistance of the cell is 0.5 Ω. The amount of charge on the capacitor plate is

In the diagram a graph between the intensity of X-rays emitted by a molybdenum target and the wavelength is shown, when electrons of 30 keV are incident on the target. In the graph one peak is of $\mathrm{K}_\alpha$ line and the other peak is of $\mathrm{K}_\beta$ line

A rectangular loop of sides $12 \mathrm{~cm}$ and $5 \mathrm{~cm}$, with its sides parallel to the $x$-axis and $y$-axis respectively moves with a velocity of $5 \mathrm{~cm} / \mathrm{s}$ in the positive $\mathrm{x}$ axis direction, in a space containing a variable magnetic field in the positive $z$ direction. The field has a gradient of $10^{-3} \mathrm{~T} / \mathrm{cm}$ along the negative $\mathrm{x}$ direction and it is decreasing with time at the rate of $10^{-5} \mathrm{~T} / \mathrm{s}$. If the resistance of the loop is $6 \mathrm{~m} \Omega$, the power dissipated by the loop as heat is______ $\times 10^{-9} \mathrm{~W}$.

The momentum of a photon is $3.3 \times {10^{ - 29}}kg - m/sec$. Its frequency will be