Physics Electromagnetism questions from JEE Main 2008.
A $5 \mathrm{~V}$ battery with internal resistance $2 \Omega$ and a $2 \mathrm{~V}$ battery with internal resistance $1 \Omega$ are connected to a $10 \Omega$ resistor as shown in the figure. The current in the $10 \Omega$ resistor is 
A horizontal overhead power line is at a height of $4 \mathrm{~m}$ from the ground and carries a current of $100 \mathrm{~A}$ from east to west. The magnetic field directly below it on the ground is $\left(\mu_0=4 \pi \times 10^{-7} \mathrm{~T} \mathrm{~m} \mathrm{~A}^{-1}\right)$
A parallel plate capacitor with air between the plates has a capacitance of $9 \mathrm{pF}$. The separation between its plates is ' $d$ '. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $k_1=3$ and thickness $\frac{d}{3}$ while the other one has dielectric constant $\mathrm{k}_2=6$ and thickness $\frac{2 \mathrm{~d}}{3}$. Capacitance of the capacitor is now
A thin spherical shell of radius $R$ has charge $Q$ spread uniformly over its surface. Which of the following graphs most closely represents the electric field $E(r)$ produced by the shell in the range $0 \leq$ $r < \infty$, where $r$ is the distance from the centre of the shell?
Paragraph: Consider a block of conducting material of resistivity ' $\rho$ ' shown in the figure. Current 'l' enters at 'A' and leaves from ' $\mathrm{D}$ '. We apply superposition principle to find voltage ' $\Delta \mathrm{V}$ ' developed between ' $\mathrm{B}$ ' and ' $\mathrm{C}$ '. The calculation is done in the following steps: (i) Take current 'l' entering from 'A' and assume it to spread over a hemispherical surface in the block. (ii) Calculate field $E(r)$ at distance ' $r$ ' from $A$ by using Ohm's law $E=\rho j$, where $j$ is the current per unit area at ' $r$ '. (iii) From the ' $r$ ' dependence of $E(r)$, obtain the potential $V(r)$ at $r$. (iv) Repeat (i), (ii) and (iii) for current 'l' leaving ' $D$ ' and superpose results for ' $A$ ' and ' $D$ '. Question: $\Delta \mathrm{V}$ measured between $\mathrm{B}$ and $\mathrm{C}$ is
Paragraph: Consider a block of conducting material of resistivity ' $\rho$ ' shown in the figure. Current 'l' enters at 'A' and leaves from ' $\mathrm{D}$ '. We apply superposition principle to find voltage ' $\Delta \mathrm{V}$ ' developed between ' $\mathrm{B}$ ' and ' $\mathrm{C}$ '. The calculation is done in the following steps: (i) Take current 'l' entering from 'A' and assume it to spread over a hemispherical surface in the block. (ii) Calculate field $E(r)$ at distance ' $r$ ' from $A$ by using Ohm's law $E=\rho j$, where $j$ is the current per unit area at ' $r$ '. (iii) From the ' $r$ ' dependence of $E(r)$, obtain the potential $V(r)$ at $r$. (iv) Repeat (i), (ii) and (iii) for current 'l' leaving ' $D$ ' and superpose results for ' $A$ ' and ' $D$ '. Question: For current entering at $A$, the electric field at a distance ' $r$ ' from $A$ is
Relative permittivity and permeability of a material are $\varepsilon_{\mathrm{r}}$ and $\mu_{\mathrm{r}}$, respectively. Which of the following values of these quantities are allowed for a diamagnetic material?
Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross sectional area $A=$ $10 \mathrm{~cm}^2$ and length $=20 \mathrm{~cm}$. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is $\left(\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}\right)$