A coil of wire has 10 loops. Each loop has an area of 1.5 ｘ10⁻³ m².  A magnetic field is perpendicular to the surface of each loop at all times. If the magnetic field is changed from 0.05 T to 0.06 T in 0.1 sec. Find the average emf induced in the coil during this time. (Answer: 1.5 ｘ10⁻³ V). 



Data Given:

Number of loop = N = 10  

Area of each loop = A = 1.5 ｘ10⁻³ m²

Change in magnetic field ΔB = 0.06 T - 0.05 T = 0.01 T 

Time interval = △t = 0.1 s


To Find:


Induced e.m.f. in the coil = Ɛ = ?


Solution:

Using the following relation

Ɛ = -N `\frac {Δф}{Δt}`

where Δф = ΔB . A = ΔB A 

taking absolute value the negative sign will become positive

|Ɛ| = |-N  `\frac {ΔB A }{Δt}`|

Ɛ = N  `\frac {ΔB A}{Δt}`

by putting the corresponding values

Ɛ = 10 ｘ `\frac {0.01 T ｘ 1.5 ｘ10⁻³ m² }{0.1 s}`

Ɛ = `\frac {0.15 ｘ10⁻³ T m²}{0.1 s}`

Ɛ = 1.5 ｘ10⁻³ V -----------Ans.




Unit Conversion:

Tesla = T = N A⁻¹ m⁻¹
Volt = V= N m C⁻¹
C⁻¹=A⁻¹s⁻¹




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