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.

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 = ?  

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

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