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PHYSICS, M4 EQ-Bank 4

A wire with a current of \(I\) amps running through it was measured to have a magnetic field strength of 2 × 10\(^{-3}\) T at a distance of \( r\) metres from the wire.

If the current through the wire is halved and the distance \(r\) is increased to \(3r\), find the new magnetic field strength measured.  (2 marks)

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\(3.33 \times 10^{-4}\ \text{T}\)

Show Worked Solution

\(B_{\text{initial}}= 2 \times 10^{-3} = \dfrac{\mu_0 \times I}{2\pi \times r}\)

\(\text{Find}\ B\ \text{when}\ I → \dfrac{I}{2},\ \text{and}\ r → 3r:\)

\(B_{\text{new}}\) \(=\dfrac{\mu_0 \times \frac{I}{2}}{2\pi \times 3r}\)  
  \(=\dfrac{1}{6} \times \dfrac{\mu_0 \times I}{2\pi \times r}\)  
  \(=\dfrac{1}{6} \times 2 \times 10^{-3}\)  
  \(=3.33 \times 10^{-4}\ \text{T}\)  

PHYSICS, M4 EQ-Bank 1

Determine the magnetic field intensity within a solenoid with 20 coils and a length of 15 cm, given that a direct current of 4 amperes flows through it.   (3 marks)

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\(6.7 \times 10^{-4}\ \text{T}\)

Show Worked Solution
\(B\) \(=\dfrac{\mu_0 N I}{L}\)  
  \(=\dfrac{4\pi \times 10^{-7} \times 20 \times 4}{0.15}\)  
  \(=6.7 \times 10^{-4}\ \text{T}\)  

PHYSICS, M4 2023 VCE 3a

Two long, straight current-carrying wires, \(\text{P}\) and \(\text{Q}\), are parallel, as shown below. The current in the wires is the same in magnitude and opposite in direction.

Figure 2b shows the wires as viewed from above.
 

On Figure 2b, sketch the magnetic field around the wires, showing the direction of the magnetic field. Use at least five field lines.  (3 marks)

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Show Worked Solution

→ Use the right-hand grip rule to determine the directions of the magnetic fields surrounding the currents, remembering that an \(X\) means “into the page” and the dot means “out of the page”.

→ As the distance from the wire increases the field strength decreases according to the inverse square law and therefore does not decrease at a linear rate (as seen in the diagram by the greater distances between field lines the further from the wires).

♦ Mean mark 48%.

PHYSICS, M4 2018 VCE 3 MC

A straight wire carries a current of 10 A.

Which one of the following diagrams best shows the magnetic field associated with this current?
 

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\(A\)

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→ Using the right hand grip rule, the thumb points up and the fingers curl in an anticlockwise direction as seen from above.

\(\Rightarrow A\)

PHYSICS, M4 2014 HSC 23

A square current-carrying wire loop is placed near a straight current-carrying conductor, as shown in the diagram.

Explain how the current in the wire loop affects the straight conductor.  (3 marks)

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→ Using the right hand rule on side \(BC\), the current produces a magnetic field going into the page on the bottom side of it and a magnetic field going out of the page on the top side of it.

→ Using the right hand rule on side \(DA\), the current produces a magnetic field going into the page on the top side of it and a magnetic field going out of the page on the bottom side of it.

→ The straight current carrying conductor itself will produce a magnetic field going into the page on the bottom side of it and a magnetic field going out of the page on the top side of it, same as side \(BC\). 

→ Therefore, the straight conductor and side \(BC\) will be attracted to each other and the straight conductor and side \(DA\) will repel each other.

→ As \(BC\) is closer to the straight conductor than \(DA\), the overall net force on the straight conductor will be an attractive force towards the wire.

→ Note the perpendicular sides \(AB\) and \(CD\) have no effect on the straight conductor.

Show Worked Solution

→ Using the right hand rule on side \(BC\), the current produces a magnetic field going into the page on the bottom side of it and a magnetic field going out of the page on the top side of it.

→ Using the right hand rule on side \(DA\), the current produces a magnetic field going into the page on the top side of it and a magnetic field going out of the page on the bottom side of it.

→ The straight current carrying conductor itself will produce a magnetic field going into the page on the bottom side of it and a magnetic field going out of the page on the top side of it, same as side \(BC\). 

→ Therefore, the straight conductor and side \(BC\) will be attracted to each other and the straight conductor and side \(DA\) will repel each other.

→ As \(BC\) is closer to the straight conductor than \(DA\), the overall net force on the straight conductor will be an attractive force towards the wire.

→ Note the perpendicular sides \(AB\) and \(CD\) have no effect on the straight conductor.

♦ Mean mark 51%.