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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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Irina-Kira [14]

Answer:

the branch currents are as follows:

  top left: I2 = 0.625 A

  middle left: I1 = 2.500 A

  bottom left: I1-I2 = 1.875 A

  top center: I2+I3 = 2.500 A

  bottom center: I2+I3-I1 = 0 A

  right: I3 = 1.875 A

Explanation:

You can write the KVL equations:

Top left loop:

  I2(4) +(I2 +I3)(2) +I1(1) = 10

Bottom left loop:

  (I1-I2)(4) +(I1-I2-I3)(2) +I1(1) = 10

Right loop:

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In matrix form, the equations are ...

  \left[\begin{array}{ccc}1&6&2\\7&-6&-2\\-2&4&4\end{array}\right]\cdot\left[\begin{array}{c}I_1\\I_2\\I_3\end{array}\right] =\left[\begin{array}{c}10\\10\\5\end{array}\right]

These equations have the solution ...

  \left[\begin{array}{c}I_1\\I_2\\I_3\end{array}\right] =\left[\begin{array}{c}2.500\\0.625\\1.875\end{array}\right]

This means the branch currents are as follows:

  top left: I2 = 0.625 A

  middle left: I1 = 2.500 A

  bottom left: I1-I2 = 1.875 A

  top center: I2+I3 = 2.500 A

  bottom center: I2+I3-I1 = 0 A

  right: I3 = 1.875 A

_____

This can be worked almost in your head by using the superposition theorem. When the 5V source is shorted, the 10V source is supplying (I1) to a circuit that is the 4 Ω and 2 Ω resistors in parallel with their counterparts, and that 2+1 Ω combination in series with 1 Ω for a total of a 4Ω load on the 10 V source. That is, I1 due to the 10V source is 2.5 A, and it is nominally split in half through the upper and lower branches of the circuit. There is no current flowing through the (shorted) 5 V source branch.

When the 10V source is shorted, the 5V source is supplying a 4 +4 Ω branch in parallel with a 2 +2 Ω branch, a total load of 8/3 Ω. This makes the current from that source (I3) be 5/(8/3) = 15/8 = 1.875 A. There is zero current from this source through the 1 Ω resistor.

Nominally, the current from the 5V source splits 2/3 through the 2 Ω branch and 1/3 through the 4 Ω branch.

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