Calculate the electric field on the axis of a very long uniformly charged, thin rod at a distance r from one end. The charge per unit length of the rod is $\lambda$[This question is only for Dropper and XII batch]

1. $\frac{2k\lambda }{r}$

2. $\frac{k\lambda }{r}$

3. $\frac{k\lambda }{2r}$

4. $\frac{k\lambda }{4r}$

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Find electric field at the centre of arc which subtends '$\theta$' angle at centre

[This question is only for Dropper and XII batch]

1.

2. $\frac{2k\lambda }{r}\mathrm{sin}\frac{\theta }{4}$

3. $\frac{2k\lambda }{r}\mathrm{sin}\frac{\theta }{2}$

4. $\frac{2k\lambda }{r}\mathrm{sin}2\theta$

Concept Questions :-

Integration
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Find electric field due to a uniformly charged, long and thin rod

[This question is only for Dropper and XII batch]

1. $\frac{k\lambda }{r}$

2. $\frac{k\lambda }{2r}$

3. $\frac{2k\lambda }{r}$

4. $\frac{k\lambda }{4r}$

Concept Questions :-

Integration
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A ball of radius R carries a positive charge throughout its volume, such that the volume density of charge depends on distance r from the ball's centre as $\rho ={\rho }_{0}\left(1-\frac{r}{R}\right)$, where ${\rho }_{0}$ is a constant. Assuming the permittivity of ball to be one, find magnitude of electric field as a function of distance r, both inside  the ball. [This question is only for Dropper and XII batch]

1.$\frac{{\rho }_{0}r}{3{\epsilon }_{0}}$

2. $\frac{{\rho }_{0}\left(4rR-3{r}^{2}\right)}{12{\epsilon }_{0}R}$

3. $\frac{{\rho }_{0}\left(4rR-3{r}^{2}\right)}{3{\epsilon }_{0}R}$

4. $\frac{{\rho }_{0}\left(4rR-5{r}^{2}\right)}{3{\epsilon }_{0}R}$

Concept Questions :-

Integration
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The electric field vector in a region given by $\stackrel{\to }{E}=\left(3\stackrel{^}{i}+4y\stackrel{^}{j}\right)V{m}^{-1}$. Calculate the potential at (1m, 1m) taking potential at origin to be zero. [This question is only for Dropper and XII batch]

1. 5V

2. 3V

3. -1V

4. -5V

Concept Questions :-

Integration
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Each of a parallel-plate air capacitor has an area S. What amount of work has to be performed to slowly increase the distance between the plates from . If the voltage across the capacitor, which is equal to V, is kept constant in the process. [This question is only for Dropper and XII batch]

1. $\frac{{\epsilon }_{0}SV}{2}$

2. ${\epsilon }_{0}S{V}^{2}\left[\frac{1}{{x}_{1}}-\frac{1}{{x}_{2}}\right]$

3. $\frac{{\epsilon }_{0}S{V}^{2}}{2}\left[\frac{1}{{x}_{1}}-\frac{1}{{x}_{2}}\right]$

4. ${\epsilon }_{0}SV$

Concept Questions :-

Integration
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Using the concept of energy density, find the total energy stored by a shell of radius R and charge Q. [This question is only for Dropper and XII batch]

1. $\frac{{Q}^{2}}{{\mathrm{\pi \epsilon }}_{0}\mathrm{R}}$

2. $\frac{{Q}^{2}}{2{\mathrm{\pi \epsilon }}_{0}\mathrm{R}}$

3. $\frac{{Q}^{2}}{4{\mathrm{\pi \epsilon }}_{0}\mathrm{R}}$

4. $\frac{{Q}^{2}}{8{\mathrm{\pi \epsilon }}_{0}\mathrm{R}}$

Concept Questions :-

Integration
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Electric field is given by E $=\frac{100}{{x}^{2}}$ . Find the potential difference between x= 10 and x= 20 m. [This question is only for Dropper and XII batch]

1. 5 V

2. 10 V

3. 15 V

4. 20 V

Concept Questions :-

Integration
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The temperature of n moles of an ideal gas is increased from  through a process $P=\frac{\alpha }{T}$ . Find the work done by the gas. [This question is only for Dropper and XII batch]

1. $\frac{nR{T}_{0}}{2}$

2. $nR{T}_{0}$

3. $\frac{3}{2}nR{T}_{0}$

4. 2 $nR{T}_{0}$

Concept Questions :-

Integration
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An isolated container at 127$°C$ contains an ice cube of mass 100 g at 0$°C$. The specific heat C of container varies with temperature according to relation C= a+bT, where a= 0.1 kcal/kg-K and b= 40 m cal/kg K. Find the mass of container, if the final temperature of container is 300 K.
[Take ${L}_{F}$= 80 cal/g and specific heat of water 1 cal/g K]

[This question is only for Dropper and XII batch]

1. 500 g

2. 720 g

3. 940 g

4. 1200 g

Concept Questions :-

Integration
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