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Q. No.The charge is distributed within a sphere of radius \({R} \) with a volume charge density; \({ \rho(r)= {\frac{A}{r^2}}e^{\left(\frac{-2r}{a}\right)}}, \) where \({A}\) and \(a \) are constants. If \({Q}\) is the total charge of this charge distribution, the radius \({R}\) is:
1. \(a ~\text{log}\left(1-\dfrac{Q}{2 \pi aA}\right) \)
2. \(\dfrac{a}{2} ~\text{log}\left(\dfrac{1}{1-\dfrac{Q}{2 \pi aA}}\right)\)
3. \(a~\text{log}\left(\dfrac{1}{1-\dfrac{Q}{2 \pi aA}}\right) \)
4. \(\dfrac{a}{2} ~\text{log}\left(1-\dfrac{1}{2 \pi aA}\right) \)
1. \(a ~\text{log}\left(1-\dfrac{Q}{2 \pi aA}\right) \)
2. \(\dfrac{a}{2} ~\text{log}\left(\dfrac{1}{1-\dfrac{Q}{2 \pi aA}}\right)\)
3. \(a~\text{log}\left(\dfrac{1}{1-\dfrac{Q}{2 \pi aA}}\right) \)
4. \(\dfrac{a}{2} ~\text{log}\left(1-\dfrac{1}{2 \pi aA}\right) \)
Subtopic: Electric Charge |
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Level 2: 60%+
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A parallel plate capacitor with plates of area \(\mathrm{1 ~m^2 }\) each, are at a separation of \(\mathrm{0.1~ m.}\) If the electric field between the plates is \(\mathrm{100~ N/C,}\) the magnitude of charge on each plate is:
1. \(\mathrm{7.85\times 10^{-10}C}\)
2. \(\mathrm{6.85\times 10^{-10}C}\)
3. \(\mathrm{8.85\times 10^{-10}C}\)
4. \(\mathrm{9.85\times 10^{-10}C}\)
1. \(\mathrm{7.85\times 10^{-10}C}\)
2. \(\mathrm{6.85\times 10^{-10}C}\)
3. \(\mathrm{8.85\times 10^{-10}C}\)
4. \(\mathrm{9.85\times 10^{-10}C}\)
Subtopic: Electric Charge |
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Level 2: 60%+
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On vehicles that carry inflammable fluids, you might notice metallic chains dangling down, touching the ground. Why are they actually used?
| 1. | Just a random custom. |
| 2. | To alert other vehicles. |
| 3. | To discharge static charges produced due to friction. |
| 4. | Just for fashion vibes. |
Subtopic: Electric Charge |
91%
Level 1: 80%+
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Electric charge is transferred to an irregular metallic disk as shown in figure:
If \(σ_1, σ_2, σ_3 \) and \(σ_4 \) are charge densities at given points then:
Choose the correct answer from the options given below:
If \(σ_1, σ_2, σ_3 \) and \(σ_4 \) are charge densities at given points then:
| \(\mathrm{A}.\) | \(σ_1 > σ_3; σ_2 = σ_4 \) |
| \(\mathrm{B}.\) | \(σ_1 > σ_2; σ_3 > σ_4 \) |
| \(\mathrm{C}.\) | \(σ_1 > σ_3 > σ_2 = σ_4 \) |
| \(\mathrm{D}.\) | \(σ_1 < σ_3 < σ_2 = σ_4 \) |
| \(\mathrm{E}.\) | \(σ_1 = σ_2 = σ_3 = σ_4 \) |
| 1. | \(\mathrm{A, B~\text{and}~C}\) Only | 2. | \(\mathrm{A~\text{and}~C}\) Only |
| 3. | \(\mathrm{ D~\text{and}~E}\) Only | 4. | \(\mathrm{B~\text{and}~C}\) Only |
Subtopic: Electric Charge |
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Level 3: 35%-60%
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- 1(current)
Q. No.
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