Question

A 15cm×15cm square loop lies in the xy-plane. The magnetic field

in this region of space is B=(0.27ti^+0.53t2k^)T
B=(0.27ti^+0.53t2k^)T, where t is in s.
What is the E induced in the loop at t = 0.5s

Answer 1

The electric field induced in the loop at t = 0.5s can be found using Faraday's Law of electromagnetic induction.

Step-by-step explanation:

The electric field induced in the loop at t = 0.5s can be found using Faraday's Law of electromagnetic induction. Faraday's Law states that the induced emf (ε) in a loop is equal to the negative rate of change of magnetic flux through the loop. In this case, the magnetic field is changing with time, so the induced emf can be calculated as:

ε = -dΦ/dt

Since the loop is a square with sides of 15cm, the area of the loop is A = (15cm)(15cm) = 225cm². The magnetic flux (Φ) through the loop is given by Φ = B⋅A.

At t = 0.5s, substitute the given magnetic field values into the equation to find the induced emf:

ε = -d(0.27t)i/dt |t=0.5s