Question

A coil of area of cross-section 0.5 m² is placed in a magnetic field acting normally to its plane. The field varies as B = 0.5t² + 2t, where B is in tesla and t in seconds. The emf induced in the coil at t = 1s is ______.

पर्याय

• 0.5 V

• 1.0 V

• 1.5 V

• 3.0 V

Answer 1

A coil of area of cross-section 0.5 m² is placed in a magnetic field acting normally to its plane. The field varies as B = 0.5t² + 2t, where B is in tesla and t in seconds. The emf induced in the coil at t = 1s is 1.5 V.

Explanation:

When a coil is placed in a changing magnetic field, an electromotive force (EMF) is induced in the coil according to Faraday's Law of Electromagnetic Induction, which states that:

EMF(E) = `-(dΦ)/dt`

Magnetic flux (Φ) is given by: Φ = B ⋅ A

• Area (A) = 0.5 m²
• Magnetic field (B) = 0.5t² + 2t (in tesla)

Substitute this:

Φ = (0.5t² + 2t) ⋅ 0.5

Φ = 0.25t² + t

Differentiate the flux with respect to time to find the induced EMF:

`E = -(dΦ)/dt`

`(dΦ)/dt = d/dt (0.25t^2+t) = (0.5t) + 1`

At t = 1 second:

E = −(0.5 × 1 + 1)

E = −(0.5 + 1) = −1.5 V

Since we usually consider the magnitude of the induced EMF:

∣E∣ = 1.5 V