Irodov – JEE First

Ampere’s law and symmetry

October 31st, 2022jeefirst0 Comments

Problem 3.231 from Irodov.

A current $I$ flows along a lengthy straight wire, as shown in the figure below. From the point O the current spreads radially all over an infinite conducting plane perpendicular to the wire. Find the magnetic field above and below the plane.

Rendered by QuickLaTeX.com — A wire carrying current to an infinite conducting plane. We indicate the radial current on the plane with a few lines, but there is current flowing along every point of the plane.

Solution:

We will use this problem to demonstrate the use of Ampere’s law, starting with some simple scenarios. Our goal is to understand …

Terminal velocity in a magnetic field

February 23rd, 2022jeefirst0 Comments

A copper connector of mass $m$ slides down two smooth copper bars, set at an angle $\alpha$ to the horizontal, due to gravity (see figure). At the top the bars are interconnected through a resistance $R$ . The separation between the bars is $\ell$ . The system is located in a uniform magnetic field of induction $B$ , perpendicular to the plane in which the connector slides. The resistance of the bars, the connector and the sliding contacts, as well as the self-inductance of the loop are assumed to be negilible. If the connector is released from rest at $t=0$ ,

Find the velocty $v(t)$ of

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Electromagnetic induction in a twisted loop

February 21st, 2022jeefirst0 Comments

JEE Advanced 2017 Paper 1, Question 5

A circular insulated copper wire loop is twisted to form two loops of area $A$ and $2 A$ as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field ${\bf B}$ points into the plane of the paper. At $t=0$ , the loop starts rotating about the common diameter as axis with a constant angular velocity $\omega$ in the magnetic field. Which of the following options is/are correct?

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The emf induced in the loop is proportional to the sum

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An infinite ladder of resistors

January 16th, 2022jeefirst0 Comments

Problem 3.152 of Irodov

The figure below shows an inifite circuit formed by the repetition of the same link, consisting of resistance $R_1 = 4.0 \ \Omega$ and $R_2 = 3.0 \ \Omega$ . Find the resistance of this circuit between points $A$ and $B$ .

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Solution

Let’s denote the resistance between the points $A$ and $B$ by $R_{AB}$ . Since the circuit is infinite, removing the first $R_1$ and $R_2$ resistors gives the same arrangement back again — the arrangement is self-similar. That means, the resistance between the points $C$ and $D$ is just $R_{AB}$ without the left-most $R_1$ and $R_2$ resistors, and we may redraw the circuit as shown below.

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It is now straightforward to calculate the resistance,

(1) …