Magnetic field induction at the centre of a c | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The magnetic field induction $B$ at the centre of a circular coil is given by the formula:$B = \frac{\mu_0 I}{2r} \quad \dots (i)$We know the rela

Vedclass · Accepted Answer

$\frac{1}{\varepsilon_0 10^{16}}$

Vedclass · Answer

(A) The magnetic field induction $B$ at the centre of a circular coil is given by the formula:$B = \frac{\mu_0 I}{2r} \quad \dots (i)$We know the relationship between the speed of light $c$,permeability $\mu_0$,and permittivity $\varepsilon_0$ is:$c^2 = \frac{1}{\mu_0 \varepsilon_0} \implies \mu_0 = \frac{1}{\varepsilon_0 c^2}$Substituting this into equation $(i)$:$B = \left( \frac{1}{\varepsilon_0 c^2} ight) \frac{I}{2r}$Given values: $I = 0.9 \,A$,$r = 5 \,cm = 5 	imes 10^{-2} \,m$,$c = 3 	imes 10^8 \,ms^{-1}$.$B = \frac{1}{\varepsilon_0 (3 	imes 10^8)^2} 	imes \frac{0.9}{2 	imes 5 	imes 10^{-2}}$$B = \frac{1}{\varepsilon_0 	imes 9 	imes 10^{16}} 	imes \frac{0.9}{10 	imes 10^{-2}}$$B = \frac{1}{\varepsilon_0 	imes 9 	imes 10^{16}} 	imes \frac{0.9}{0.1} = \frac{1}{\varepsilon_0 	imes 9 	imes 10^{16}} 	imes 9$$B = \frac{1}{\varepsilon_0 	imes 10^{16}}$

Magnetic field induction at the centre of a circular coil of radius $5 \,cm$ and carrying a current $0.9 \,A$ is (in $SI$ units) (where $\varepsilon_0$ is the absolute permittivity of air in $SI$ units,and the velocity of light $c = 3 \times 10^8 \,ms^{-1}$)

Similar Questions

Find the magnetic field at point $P$ in the given diagram. The wire carries a current $i$.

What should be the current $i$ (in $A$) in a circular coil of radius $5\,cm$ to annul the horizontal component of Earth's magnetic field ${B_H} = 5 \times {10^{ - 5}}\,T$?

$A$ long straight wire, carrying current $I,$ is bent at its midpoint to form an angle of $45^{\circ}.$ The magnetic field induction at point $P,$ at a distance $R$ from the point of bending, is equal to:

$A$ current $i$ is flowing in a straight conductor of length $L$. The magnetic induction at a point distant $\frac{L}{4}$ from its centre will be

Biot-Savart law indicates that the moving electrons (velocity $\vec{v}$) produce a magnetic field $\vec{B}$ such that

Vedclass Test Series

Exam Paper Generator

Online Exam Module