A thin flexible wire of length L is connected to two adjacent
fixed points and carries a current I in the clockwise direction,
as shown in the figure. When the system is put in a uniform
magnetic field of strength B going into the plane of the paper,
the wire takes the shape of a circle. The tension in the wire is
- IBL
- $\frac{IBL}{\pi}$
- $\frac{IBL}{2 \pi}$
- $\frac{IBL}{4 \pi}$
The Correct Option is C
Solution and Explanation
$\therefore \, \, \, \, \, \, \, R= L / 2\pi$
$ \, \, \, \, \, \, \, \, \, \, 2T sin(d
heta) = F_m$
For small angles, $sin(d
heta) \approx d
heta$
$\therefore \, \, \, \, \, \, \, 2T (d
heta) = I (dL) B \, sin \, 90^{\circ} $
$ \, \, \, \, \, \, \, \, \, \, \, \, \, = I (2R \, \cdot d
heta) \cdot B$
$\therefore \, \, \, \, \, \, \, \, \, \, \, T = IRB = \frac{ILB}{2 \pi}$
$\therefore \, $ Correct option is (c)
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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.