The magnetic flux through a coil perpendicular to its plane is varying according to the relation \(\varphi = 5t^3 + 4t^2 + 2t - 5\) Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at t = 2 s will be,
- 15.6 A
- 16.6 A
- 17.6 A
- 18.6 A
The Correct Option is A
Solution and Explanation
\(\text{EMF} = -\frac{d\Phi}{dt} = -(15t^2 + 8t + 2)\)
\(i = \frac{\lvert \text{EMF} \rvert}{R} = \frac{15t^2 + 8t + 2}{5}\)
at t = 2
\(i(t=2) = \frac{15(2)^2 + 8(2) + 2}{5} \)
\(i=15.6A\)
So,correct option is (A)
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Concepts Used:
Magnetic Flux
Magnetic flux refers to the amount of magnetic field passing through a given area. It is a measure of the strength of the magnetic field over a particular surface. The unit of magnetic flux is the Weber (Wb).
Magnetic flux is determined by the strength of the magnetic field and the area over which it is applied. The magnetic field is a vector field that exerts a force on moving charged particles. It is represented by magnetic lines of force that show the direction and intensity of the field. The magnetic flux passing through a surface is proportional to the number of magnetic field lines passing through that surface.
The magnetic flux through a closed surface is always zero, as the field lines entering the surface must also exit the surface. This principle is known as Gauss's law for magnetism. However, for an open surface, the magnetic flux can be calculated using the formula:
\(Φ = B.A.cosθ\)
where Φ is the magnetic flux, B is the magnetic field, A is the area of the surface, and θ is the angle between the magnetic field and the surface normal.
Also Read: Unit of Magnetic Flux
Magnetic flux has various applications in physics and engineering, including electromagnetic induction, which is used in electrical generators and transformers. The amount of magnetic flux generated by a magnet can also be used to measure its strength, and it is often used in magnetic imaging techniques such as magnetic resonance imaging (MRI).