A conducting rod of 1 m length and 1 kg mass is suspended by two vertical wires through the en

step 1 Hello and welcome to this video solution of numerate. So here a conducting rod of one meter leng

A conducting rod of 1 m length and 1 kg mass is suspended...

A conducting rod of $1 \mathrm{~m}$ length and $1 \mathrm{~kg}$ mass is suspended by two vertical wires through the ends. An external magnetic fields of $2 \mathrm{~T}$ is applied normal to the rod. Now the current to be passed through the rod so as to make the tension in the wires zero is (Take $\left.g=10 \mathrm{~ms}^{-2}\right) \quad[$ Kerala CET 2007] (a) $0.5 \mathrm{~A}$ (b) $15 \mathrm{~A}$ (c) $5 \mathrm{~A}$ (d) $1.5 \mathrm{~A}$ (e) $15 \mathrm{~A}$

A conducting rod of $1 \mathrm{~m}$ length and $1 \mathrm{~kg}$ mass is suspended by two vertical wires through the ends. An external magnetic fields of $2 \mathrm{~T}$ is applied normal to the rod. Now the current to be passed through the rod so as to make the tension in the wires zero is (Take $\left.g=10 \mathrm{~ms}^{-2}\right) \quad[$ Kerala CET 2007]
(a) $0.5 \mathrm{~A}$
(b) $15 \mathrm{~A}$
(c) $5 \mathrm{~A}$
(d) $1.5 \mathrm{~A}$
(e) $15 \mathrm{~A}$

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Key Concepts

Magnetic Field Interaction with Conductors

This concept explains that when a conductor carrying an electrical current is placed in a magnetic field, the interaction results in a force on the conductor as described by the Lorentz force. The direction and magnitude of this force depend on the orientation of the conductor relative to the magnetic field and are essential in applications where magnetic forces are used to oppose or balance other forces, such as gravity.

Lorentz Force

This fundamental concept in electromagnetism states that a current-carrying conductor placed in a magnetic field experiences a force. The magnitude of this force is given by the product of the current (I), the length of the conductor (L), and the magnetic field strength (B) when the conductor is perpendicular to the field. This concept is crucial when determining how an applied current can counteract gravitational forces acting on the rod.

Equilibrium of Forces

In mechanics, equilibrium refers to the state where all forces acting on an object cancel each other out, resulting in no net acceleration. In the context of the problem, achieving equilibrium by making the tension in the suspension wires zero involves balancing the gravitational force (mg) with the magnetic force (I L B), ensuring that the rod is in static equilibrium.

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