Question:
A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
Updated On: May 16, 2022
- 0.2 T
- 0.3 T
- 0.4 T
- 0.05 T
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The Correct Option is D
Solution and Explanation
$NBi \, A \sin \,
heta= \tau \hspace25mm ...(i) $
N, B, i and A are constants
$\therefore \hspace15mm sin
\theta \propto 0.3 $
$\hspace15mm cos
\theta \propto 0.4 $
$\hspace15mm tan \theta = \frac {3}{4} $
From E (i)
$\hspace15mm sin \,
heta = \frac {3}{5} $
$\hspace15mm B= \frac {\tau}{NiAsin \,
heta}$
$\hspace10mm B= \frac {0.3 \times 5}{100\times5\times2\times10^{-2}\times3}=0.05 \, T$
heta= \tau \hspace25mm ...(i) $
N, B, i and A are constants
$\therefore \hspace15mm sin
\theta \propto 0.3 $
$\hspace15mm cos
\theta \propto 0.4 $
$\hspace15mm tan \theta = \frac {3}{4} $
From E (i)
$\hspace15mm sin \,
heta = \frac {3}{5} $
$\hspace15mm B= \frac {\tau}{NiAsin \,
heta}$
$\hspace10mm B= \frac {0.3 \times 5}{100\times5\times2\times10^{-2}\times3}=0.05 \, T$
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Concepts Used:
Gauss Law
Gauss law states that the total amount of electric flux passing through any closed surface is directly proportional to the enclosed electric charge.
Gauss Law:
According to the Gauss law, the total flux linked with a closed surface is 1/ε0 times the charge enclosed by the closed surface.
For example, a point charge q is placed inside a cube of edge ‘a’. Now as per Gauss law, the flux through each face of the cube is q/6ε0.
Gauss Law Formula:
As per the Gauss theorem, the total charge enclosed in a closed surface is proportional to the total flux enclosed by the surface. Therefore, if ϕ is total flux and ϵ0 is electric constant, the total electric charge Q enclosed by the surface is;
Q = ϕ ϵ0
The Gauss law formula is expressed by;
ϕ = Q/ϵ0
Where,
Q = total charge within the given surface,
ε0 = the electric constant.