Question

A particle carrying a charge equal to 100 times the charge on an electron is rotating per sec in a circular path of radius 0.8 m. The value of magnetic field (Weber/m²) produced at the centre will be (μ_o = permeability of free space)
1. \(\frac{10^{-7}}{\mu_o}\)
2. 10^-17μ_o
3. 10-6μo
4. 10-7μo

Answer 1

Correct Answer - Option 2 : 10^-17μ_o

Concept:

Current: Current is defined as charge per unit time.

\(i=\frac qt\)

Magnetic field produced at the centre of current carrying circular coil is given by:

\(B=\frac{\mu_oi}{2r}\)

where i is current, r is the radius of the circular coil

Calculation:

Given:

q = 100e, t = 1 s, r = 0.8 m

Current flowing in the coil is:

\(i=\frac qt=\frac{100\;\times\; 1.6\;\times\; 10^{-19}}{1}A\)

Magnetic field produced at the centre is:

\(B=\frac{\mu_oi}{2r}\)

\(B=\frac{\mu_o\;\times\;{100\;\times \;1.6\;\times \;10^{-19}}}{2\;\times\;0.8}\)

B = 10-17μo Weber/m²