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 ______.

Options

• 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 3.0 V.

Explanation:

The magnetic flux Φ through the coil is given by the product of the magnetic field strength and the area of the coil:

`phi = vecB * vecA`

Given the magnetic field equation B = 0.5t² + 2t and the area A = 0.5 m², we can calculate the flux Φ at t = 1 second:

Φ = (0.5·(1)² + 2·1) × 0.5

Φ = (0.5 + 2) × 0.5

Φ = (2.5) × 0.5

Φ = 1.25 Wb

Now, we find the rate of change of magnetic flux `(dphi)/(dt)` by differentiating the magnetic flux equation with respect to time:

`(dphi)/(dt) = d/(dt)(0.5t^2 + 2t)`

`(dphi)/(dt) = 0.5(2t) + 2`

`(dphi)/(dt) = t + 2`

Now, we can find the emf induced in the coil at t = 1 second using Faraday's law:

`e_(emf) = (dphi)/(dt)`

`e_(emf) = -(1 + 2)`

`e_(emf) = -3 V`

Emf is induced in the coil and equals the negative rate of change of flux. The induced emf at t = 1 second is e_emf = 3 V.