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KIM [24]
3 years ago
7

An MRI technician moves his hand from a region of very low magnetic field strength into an MRI scanner's 1.80 T field with his f

ingers pointing in the direction of the field. His wedding ring has a diameter of 2.23 cm, and it takes 0.320 s to move it into the field.
1. What average current is induced in the ring in A if its resistance is 0.0100 Ω?

2. What average power is dissipated in mW?

3. What magnetic field is induced at the center of the ring in T?
Physics
1 answer:
Ghella [55]3 years ago
7 0

Given that,

Magnetic field strength is

B = 1.8T

The wedding ring has a diameter of

d = 2.23 cm = 0.023m

Time take t = 0.32 secs

A. Current induced

From ohms law

V= iR, given that R = 0.01Ω

So, we need to get the induced emf

Using

ε = -NdΦ / dt

Where Φ = BA

ε = -A ∆B / ∆t

ε = -¼πd²(B2-B1) / (t2-t1)

ε = -¼ × π × 0.023² × -1.8 / 0.32

ε = 0.0023371 V

Then

I = ε / R

I = 0.002337 / 0.01

I =0.2337 A

B. Power discippated?

Power is given as

P = iV

P = 0.2337 × 0.002337

P = 0.0005462 W

P = 0.56 mW

C. The magnetic field at the centre of the ring.

The electric field at the centre of the ring is zero because each part of the ring will cause a symmetrical opposite magnitude at every point,

Then, B = 0 T

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Suppose that the inverse market demand for silicone replacement tips for Sony earbud headphones is p ​= pN ​- 0.1Q, where p is t
lbvjy [14]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

   The effect of a change in the price of a new pair of headphones on the equilibrium price of replacement tips​ ( ​dp/dpN​) is

                   \frac{\delta p}{\delta p_N} =1

b

 The value of Q and p at equilibruim is

          Q_e = 250    and    p_d = 5

The consumer surplus is  C= 3125

The producer surplus  is   P = 375

Explanation:

      From the question we are told that

           The inverse market demand is  p_d = p_N -0.1Q

                The inverse supply function is     p_s = 2+ 0.012Q

a

The effect of change in the price  is mathematically given as

                  \frac{\delta p}{\delta p_N}

Now differntiating the inverse market demand function with respect to p_N

We get that  

                   \frac{\delta p}{\delta p_N} =1

b

   We are told that p_N =$30

        Therefore the inverse market demand becomes

                             p_d = 30 -0.1Q

At  equilibrium

                  p_d = p_s

So we have

               30 -0.1Q_e = 2+ 0.012Q_e

Where Q_e is the quantity at equilibrium

                    28 = 0.112Q_e

                     Q_e = \frac{28}{0.112}

                    Q_e = 250

Substituting the value of  Q into the equation for the inverse market demand function

                p_d = 30 - 0.1 (250 )

                    p_d = 5

Looking at the equation for p_d \ and \ p_s we see that

     For  Q =  0

             p_d = 30

             p_s =2

 And  for Q =  250

                 p_d = 5

                 p_s = 5

Hence the consumer surplus is mathematically evaluated as

           C = \frac{1}{2} * Q_e * (30 -5)

Substituting value

        C = \frac{1}{2} * 250 (30-5)

           C= 3125

And

  The  producer surplus is mathematically evaluated as

                    P = \frac{1}{2} *250 * (5-2)

                    P = 375

     

         

           

                     

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