A straight wire of mass 200 gm and length 1.5 meter carries a current of 2 Amp. It is suspended

step 1 magnetic force on straight wire f is equal to b i l f is equal to b i l sine theta is equal to 9

A straight wire of mass 200 gm and length 1.5 meter carries...

A straight wire of mass $200 \mathrm{gm}$ and length $1.5$ meter carries a current of 2 Amp. It is suspended in mid-air by a uniform horizontal magnetic field B. [take $\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right]$. The $\mathrm{B}$ is (a) $\overline{(2 / 3) \text { tes } 1 a}$ (b) $(3 / 2)$ tesla (c) $(20 / 3)$ tesla (d) (3/20) tesla

A straight wire of mass $200 \mathrm{gm}$ and length $1.5$ meter carries a current of 2 Amp. It is suspended in mid-air by a uniform horizontal magnetic field B. [take $\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right]$. The $\mathrm{B}$ is
(a) $\overline{(2 / 3) \text { tes } 1 a}$
(b) $(3 / 2)$ tesla
(c) $(20 / 3)$ tesla
(d) (3/20) tesla

Key Concepts

Lorentz Force

The Lorentz force is the force exerted on a current-carrying conductor placed in a magnetic field. The magnitude of this force is given by the equation F = I L B sin(?), where I is the current, L is the length of the conductor, B is the magnetic field strength, and ? is the angle between the current direction and the magnetic field. This concept is central to understanding how magnetic fields interact with electric currents.

Equilibrium of Forces

In many physical problems, an object is suspended or maintained in a stationary position by ensuring that the net force acting on it is zero. This requires that all forces, such as gravitational force and magnetic force, balance each other. In the context of a current-carrying wire, the upward magnetic force must equal the downward gravitational force (mg) to achieve equilibrium.

Magnetic Field

A magnetic field is a vector field that exerts a magnetic force on moving charges and magnetic dipoles. It is measured in teslas and plays a crucial role in electromagnetic interactions. In problems involving current-carrying wires, the magnetic field provides the necessary force to counteract other forces, such as gravity, when properly oriented.

Current-Carrying Conductor

A current-carrying conductor is a material through which electric charge flows. When this conductor is placed in a magnetic field, it experiences a force perpendicular to both the direction of the current and the magnetic field. This interaction is fundamental to many electromagnetic phenomena and is described by the Lorentz force law, which is used in various applications including motors, generators, and electromagnetic suspension.

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