Question:

The value of the magnetic field induction at the centre of the coil, if l = 2A, h= 10 cm. in the following figure is

Updated On: Jul 7, 2022
  • $1.14\times10^{-5}\,T$
  • $\frac{4\pi}{\mu_0}$$1.14\times10^{-5}\,T$
  • $\frac{1.14}{4\pi}$$\times10^{-5}\,T$
  • $\frac{\mu_0}{4\pi}$$2.14\times10^{-5}\,T$
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The Correct Option is A

Solution and Explanation

For the upper straight wire, $B_1 $ = 0, $\because$ $\theta$ =0 For the lower straight wire. $B_2 = \frac{\mu_0}{4 \,\pi} \left[ \frac{I}{h} \right]$ $\because$ $\phi_1$ = 90, $\phi_2$ = 0 For circular portion, $B_3 = \frac{\mu_0 }{4 \, \pi} \left[ \frac{3 \, \pi \, I}{2 \, h} \right]$ $\because$ $\beta = \frac{3 \,\pi}{2}$ and $r = h$ Hence total field, $B = \frac{\mu_0}{4 \, \pi} \left[ \frac{I}{h} \left( \frac{3\, \pi}{2} + 1 \right) \right] = 1.14 \times 10^{-5}$ T Perpendicular to the plane of the figure and directed outward
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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.