Question:
A conducting circular loop of radius r carries a constant current z. It is placed in a uniform magnetic field $\vec{B}_{0}$ such that $\vec{B}_{0}$ is perpendicular to the plane of the loop. The magnetic force acting on the loop is
A conducting circular loop of radius r carries a constant current z. It is placed in a uniform magnetic field $\vec{B}_{0}$ such that $\vec{B}_{0}$ is perpendicular to the plane of the loop. The magnetic force acting on the loop is
Updated On: Jan 18, 2023
- $ir\, B_{0}$
- $2\pi\, ir\, B_{0}$
- zero
- $\pi\, ir\, B_{0}$
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The Correct Option is C
Solution and Explanation
The magnetic field is perpendicular to the plane of the paper. Let us consider two diametrically opposite elements. By Fleming's Left hand rule on element AB the direction of force will be Leftwards and the magnitude will be
$d F=Id/ B sin \, 90? = Id/B$
On element CD, the direction of force will be towards right on the plane of the papper and the magnitude will be dF = Id/B.
$d F=Id/ B sin \, 90? = Id/B$
On element CD, the direction of force will be towards right on the plane of the papper and the magnitude will be dF = Id/B.
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Concepts Used:
Magnetic Field
The magnetic field is a field created by moving electric charges. It is a force field that exerts a force on materials such as iron when they are placed in its vicinity. Magnetic fields do not require a medium to propagate; they can even propagate in a vacuum. Magnetic field also referred to as a vector field, describes the magnetic influence on moving electric charges, magnetic materials, and electric currents.
A magnetic field can be presented in two ways.
- Magnetic Field Vector: The magnetic field is described mathematically as a vector field. This vector field can be plotted directly as a set of many vectors drawn on a grid. Each vector points in the direction that a compass would point and has length dependent on the strength of the magnetic force.
- Magnetic Field Lines: An alternative way to represent the information contained within a vector field is with the use of field lines. Here we dispense with the grid pattern and connect the vectors with smooth lines.
Properties of Magnetic Field Lines
- Magnetic field lines never cross each other
- The density of the field lines indicates the strength of the field
- Magnetic field lines always make closed-loops
- Magnetic field lines always emerge or start from the north pole and terminate at the south pole.