# Wire loop placed in B field which is decreasing uniformly

## Homework Statement

A wire loop of area 2·0×10−4 m2
contains 40 turns, and has a total resistance of
40Ω. The plane of the loop is perpendicular to a uniform magnetic ﬁeld of magnitude
B0. The magnetic ﬁeld is now turned oﬀ such that the ﬂux through the loop drops
linearly to zero. A total charge 4·0 ×10−6 C passes around the loop. Determine B0.

None given

## The Attempt at a Solution

Ok so I think that
Emf=-N$\frac{d\Phi}{dt}$
but it says that the field drops linearly so that just becomes
Emf=-NA$\frac{\Delta B}{\Delta t}$

Also Emf=IR

So from this I equated the two but I will just end up with an expression for B0 dependent on t, and I'm not sure if this is what is wanted. I'm unsure about my use of Ohm's law here too. Thanks in advance, any help at all would be great.

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TSny
Homework Helper
Gold Member
You need one more idea: What is the relationship between the current and the total mount of charge that flows?

Current is the rate of flow of charge. So could I say from this that
B=IR/NA? Because I'll have a rate on either side of my equation?

TSny
Homework Helper
Gold Member
When you set your two expressions for Emf equal to each other and solve for ΔB, what expression do you get for ΔB?

Oh right I see, misread the question, didn't realise that it was charge not current. So you can write ΔB=QR/NA. Thanks very much!