Question

A single piece of wire is bent into the shape of Texas, with a total area of 13.3 cm2 . This Texas shaped loop is perpendicular to a magnetic field which increases uniformly in magnitude from 0.728 T to 2.27 T in a time of 3 s. The wire has a total resistance of 4 Ω. What is the current? Answer in units of mA.

Answer 1

Given Information:

Time = Δt = 3 s

Area of wire = A = 13.3 cm² = 0.00133 m²

Change in magnetic field = ΔB = (0.728 - 2.27) T

Resistance of wire = R = 4 Ω

Required Information:

Current = I = ?

Answer:

Current = 0.1708 mA

Step-by-step explanation:

We know that current is given by

I = ξ/R

Where R is the resistance and ξ is induced emf given by

ξ = -ΔΦ/Δt

Where ΔΦ is the change in flux and is given by

ΔΦ = ΔBA

ΔΦ = (0.728 - 2.27)*0.00133

ΔΦ = -0.00205 T.m²

ξ = -ΔΦ/Δt

ξ = -(-0.00205 )/3

ξ = 0.0006833 V

I = ξ/R

I = 0.0006833/4

I = 0.0001708 A

I = 0.1708 mA

Answer 2

E = induced emf = -6.82×10-⁴V

Step-by-step explanation:

Given

Area = 13.3cm³ = 13.3×10-⁴m²

ΔB = 2.27T –0.728 =1.54T

Δt = 3s

So

ΔB/Δt = 1.54/3 = 0.513T/s

ΔФ/Δt = ΔB/Δt×Area = 0.513×13.3×10-⁴ = 6.82×10-⁴Wb/s

By Faraday's law of electromagnetic induction,

E = -ΔФ/Δt = -(6.82×10-⁴) = -6.82×10-⁴V