A current of 10 A is flowing in a wire of length 1.5 m. When it is placed in a uniform magneti

step 1 So for this problem, we can start by writing down the magnetic force on a current loop, our curr

A current of 10 A is flowing in a wire of length 1.5 m....

A current of $10 \mathrm{~A}$ is flowing in a wire of length $1.5 \mathrm{~m}$. When it is placed in a uniform magnetic field of 2 Tesla then a force of $15 \mathrm{~N}$ acts on it. The angle between the magnetic field and the direction of current flow will be (a) $30^{\circ}$ (b) $45^{\circ}$ (c) $60^{\circ}$ (d) $90^{\circ}$

A current of $10 \mathrm{~A}$ is flowing in a wire of length $1.5 \mathrm{~m}$. When it is placed in a uniform magnetic field of 2 Tesla then a force of $15 \mathrm{~N}$ acts on it. The angle between the magnetic field and the direction of current flow will be
(a) $30^{\circ}$
(b) $45^{\circ}$
(c) $60^{\circ}$
(d) $90^{\circ}$

Key Concepts

Trigonometric Analysis in Physics

Trigonometric functions play a critical role in resolving the components of physical quantities. In magnetic force problems, the sine function is used to calculate the influence of the angle between the current and the magnetic field. Solving for an unknown angle often involves rearranging the force equation to isolate the sine term and then using the inverse sine function to determine the angle, a common technique in physics problem-solving.

Magnetic Force on a Current-Carrying Conductor

This concept refers to the force experienced by a conductor carrying an electric current when placed within a magnetic field. The force arises due to the interaction between the magnetic field and the moving charges in the conductor, and it is described by the equation F = I L B sin?, which relates the force (F) to the current (I), the length of the conductor (L), the magnetic field (B), and the sine of the angle (?) between the current direction and the magnetic field.

Vector Cross Product in Electromagnetism

The cross product from vector algebra is fundamental in understanding magnetic forces because it defines how two vectors interact to produce a third vector that is perpendicular to both. In electromagnetism, the direction and magnitude of the magnetic force on a current-carrying conductor are determined by the cross product of the current vector and the magnetic field vector, encapsulated in the sine term of the force equation.

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