+91-8076753736 [email protected]

Sponsor Area

Moving Charges And Magnetism

Question

Wired Faculty App

Using Biot-Savart’s law, derive an expression for the magnetic field at the centre of a circular coil of radius R, number of turns N, carrying current i.

Solution

As per Biot-Savart law, the magnetic field due to a current element

\vec{dl}

at the observation point whose position vector

\vec{r}

is given by

\vec{dB} = \frac{μ_{0} I}{4 π} . \frac{\vec{dl} \times \vec{r}}{r^{3}}

where, μ₀ is the permeability of free space.

Consider a circular loop of wire of radius 'r' carrying a current 'I' and also a current element 'dl' of the loop.

The direction of dl is along the tangent, so dl ⊥ r.

Using Biot-Savart law,

Magnetic field at the centre O due to this current element is

dB = \frac{μ_{0} I}{4 π} \frac{dl \sin 90 °}{r^{3}} = \frac{μ_{0} I}{4 π} \frac{dl}{r^{2}}

The magnetic field due to all such current elements will point into the plane of paper at the centre O.
Hence, the total magnetic field at the centre O is given by

B = \int dB = \int \frac{μ_{0} Idl}{4 {πr}^{2}}

B = \frac{μ_{0} I}{4 {πr}^{2}} \int dl = \frac{μ_{0} I}{4 {πr}^{2}} . l

= \frac{μ_{0} I}{4 {πr}^{2}} . 2 πr B = \frac{μ_{0} I}{2 r}

For a coil of N turns, magnetic field, B =

\frac{μ_{0} NI}{2 r}

.

Sponsor Area

Some More Questions From Moving Charges And Magnetism Chapter

Two moving coil meters, M₁ and M₂ have the following particulars:
R₁ = 10 Ω N₁ = 30,
A₁ = 3.6 x 10^–3 m², B₁ = 0.25 T
R₂ = 14 Ω; N₂ = 42,
A₂ = 1.8 x 10^–3 m², B₂ = 0.50 T
(The spring constants k are identical for the two meters).
Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M₂ and M_1.

Answer the following questions:
A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation