Question
A cell is connected between two points of a uniformly thick circular conductor. The magnetic field at the centre of the loop will be
✓
Answer
(a) Directions of currents in two parts are different, so directions of magnetic fields due to these currents are opposite. Also applying Ohm’s law across $AB$
${i_1}{R_1} = {i_2}{R_2} \Rightarrow {i_1}{l_2} = {i_2}{l_2}$ $\left( {\;R = \rho \frac{l}{A}} \right)$
Also ${B_1} = \frac{{{\mu _o}}}{{4\pi }} \times \frac{{{i_1}{l_1}}}{{{r^2}}}$ and ${B_2} = \frac{{{\mu _o}}}{{4\pi }} \times \frac{{{i_2}{l_2}}}{{{r^2}}}$ ($\;l = r\theta $)
$\therefore \,\frac{{{B_2}}}{{{B_1}}} = \frac{{{i_1}{l_1}}}{{{i_2}{l_2}}} = 1$
Hence, two field induction’s are equal but of opposite direction. So, resultant magnetic induction at the centre is zero and is independent of $\theta $.
${i_1}{R_1} = {i_2}{R_2} \Rightarrow {i_1}{l_2} = {i_2}{l_2}$ $\left( {\;R = \rho \frac{l}{A}} \right)$
Also ${B_1} = \frac{{{\mu _o}}}{{4\pi }} \times \frac{{{i_1}{l_1}}}{{{r^2}}}$ and ${B_2} = \frac{{{\mu _o}}}{{4\pi }} \times \frac{{{i_2}{l_2}}}{{{r^2}}}$ ($\;l = r\theta $)
$\therefore \,\frac{{{B_2}}}{{{B_1}}} = \frac{{{i_1}{l_1}}}{{{i_2}{l_2}}} = 1$
Hence, two field induction’s are equal but of opposite direction. So, resultant magnetic induction at the centre is zero and is independent of $\theta $.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Which of the following is not true for this progressive wave $y = 4\sin 2\pi \left( {\frac{t}{{0.02}} - \frac{x}{{100}}} \right)$ where $y$ and $x$ are in $cm$ & $t$ in $sec$
→A given mass $m$ of a hypothetical solid is supplied with heat continuously at a constant rate and the graph shown in the adjacent figure is plotted. If $L_f$ and $L_v$ are latent heats of fusion and latent heats of vaporization and $S_l$ and $S_s$ are specific heats of liquid and solid respectively. It can be concluded that
→An organic compound $A$, $C_5H_8O$; reacts with $H_2O$, $NH_3$ and $CH_3COOH$ as described below $A$ is
→In short wave communication waves of which of the following frequencies will be reflected back by the ionospheric layer, having electron density $10^{11}$ per $m^{3}$.......$MHz$
→A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is $v$, the total area around the fountain that gets wet is :
→An ideal monoatomic gas expands to twice its volume. If the process is isothermal, the magnitude of work done by the gas is $W_i$. If the process is adiabatic, the magnitude of work done by the gas is $W_a$. Which of the following is true?
→Assertion : A parallel plate capacitor is connected across battery through a key. A dielectric slab of dielectric constant $K$ is introduced between the plates. The energy which is stored becomes $K$ times.
→Reason : The surface density of charge onthe plate remains constant or unchanged.
Product $(A)$ and $(C)$ is
→Two plane mirrors are inclined at an angle of ${72^0}$. The number of images of a point object placed between them will be
→The graphs in figure show that a quantity $y$ varies with displacement $d$ in a system undergoing simple harmonic motion. Which graphs best represents the relationship obtained when $y$ is The total energy of the system
→