Question:
The magnetic field due to a current carrying circular loop of radius $3\, cm$ at a point on the axis at a distance of $4\, cm$ from the centre is $54 \,\mu T$. What will be its value at the centre of the loop?
The magnetic field due to a current carrying circular loop of radius $3\, cm$ at a point on the axis at a distance of $4\, cm$ from the centre is $54 \,\mu T$. What will be its value at the centre of the loop?
Updated On: Aug 1, 2022
- $250\, \mu T$
- $150\, \mu T$
- $125\, \mu T$
- $75\, \mu T$
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The Correct Option is A
Solution and Explanation
Using formula $B = \frac{\mu_{0}iR^{2}}{2\left(R^{2}+X^{2}\right)^{3/2}}$, we get
$54 = \frac{\mu_{0}i\left(3\right)^{2}}{2\left[\left(3\right)^{2}+\left(4\right)^{2}\right]^{3/ 2}}$
At the centre of the coil, $X = 0$ and $B =\frac{\mu _{0}i}{2\left(3\right)}$
Using equation $\left(i\right)$
$B = \frac{54\times5^{3}}{\left(3\right)^{2}\times3} \Rightarrow B = 250\,\mu T.$
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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.