Question

In: Physics

Problem 3. A square loop of wire is made up of 50 turns of wire, 40...

Problem 3. A square loop of wire is made up of 50 turns of wire, 40 cm on each side. The loop is immersed in a 0.4−T magnetic field perpendicular to the plane of the loop. The loop of wire has little resistance but it is connected to two resistors in parallel as shown.

When the loop of wire is rotated by 180°, how much charge flows through the circuit?

How much charge goes through the smaller resistor?

What is the direction of the induced current? Explain how you know!

Solutions

Expert Solution

An equivalent resistance will be given as :

1 / R_eq = 1 / (10 ) + 1 / (5 )

R_eq = (10/3)

R_eq = 3.33

The induced emf in the coil is given by,

= - N (_B / t)

= - N A cos 180⁰ (B / t)

= N A (B / t)

(a) When the loop of wire is rotated by 180⁰, how much charge flows through the circuit?

using an ohm's law, we have

I = / R_eq

I = [N A (B / t)] / R_eq

I t = N A B / R_eq

Q = (50) (0.4 m)² (0.4 T) / (3.33 )

Q = (3.2 mT²) / (3.33 )

Q = 0.96 C

(b) How much charge goes through the smaller resistor?

using a formula, we have

I t = N A B / R

Q = (50) (0.4 m)² (0.4 T) / (5 )

Q = (3.2 mT²) / (5 )

Q = 0.64 C

genius_generous answered 1 year ago

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