Question:
A square wire of each side l carries a current I.
The magnetic field at the mid point of the square
is
A square wire of each side l carries a current I.
The magnetic field at the mid point of the square
is
Updated On: Jun 23, 2024
- $4\sqrt{2}$$\frac{\mu_0}{4\pi}$$\frac{I}{l}$
- $8\sqrt{2}$$\frac{\mu_0}{4\pi}$$\frac{I}{l}$
- $16\sqrt{2}$$\frac{\mu_0}{4\pi}$$\frac{I}{l}$
- $32\sqrt{2}$$\frac{\mu_0}{4\pi}$$\frac{I}{l}$
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The Correct Option is B
Solution and Explanation
B = 4 $\left[ \frac{\mu_0}{4 \, \pi} \frac{I}{a} (sin \, \phi_1 + sin \, \phi_2) \right]$ ; Here $\phi_1 = \phi_2 = 45^\circ$
$\therefore$ B = $4 \times \frac{\mu_0}{4 \, \pi} \frac{I}{(l/2)} \left[ \frac{1}{\sqrt{2}} \frac{1}{\sqrt{2}}\right] = 4 \times \frac{16}{\sqrt{2}} \left[ \frac{\mu_0}{4 \, \pi}\frac{l}{l} \right] = 8 \sqrt{2} \left[ \frac{\mu_0}{4 \, \pi} \frac{l}{l} \right]$
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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.