Question 5
5
5 marks
Question 5(b)
5(b)
Two long straight vertical wires X and Y are separated by a distance of 4.5 cm , as illustrated in Fig. 5.1. The wires pass through a horizontal card PQRS. The current in wire X is 6.3 A in the upward direction. Initially, there is no current in wire Y .
structured3 marks
Question 5(b)(i)
5(b)(i)
On Fig. 5.1, sketch, in the plane PQRS , the magnetic flux pattern due to the current in wire X. Show at least four flux lines.
Easystructured3 marks
Question 5(b)(ii)
5(b)(ii)
The magnetic flux density B at a distance x from a long straight current-carrying wire is given by the expression where I is the current in the wire and \(\mu_{0}\) is the permeability of free space. Calculate the magnetic flux density at wire Y due to the current in wire X .
Mediumstructured0 marks
Answer
\(\mathrm{B}=\left(4 \pi \times 10^{-7} \times 6.3\right) /\left(2 \pi \times 4.5 \times 10^{-2}\right)\)
Question 5(c)
5(c)
The currents in the two wires in (b)(iii) are not equal. Explain whether the force per unit length on the two wires will be the same, or different.
Mediumstructured2 marks
Answer
force per unit length depends on product \(I_{\mathrm{X}} I_{\mathrm{Y}} /\) by Newton's third law / action and reaction are equal and opposite so same for both
Question 5
5
A Hall probe is placed a distance d from a long straight current-carrying wire, as illustrated in Fig.5.1. The direct current in the wire is 4.0 A . Line XY is normal to the wire. The Hall probe is rotated about the line X Y to the position where the reading \(V_{H}\) of the Hall probe is maximum.
structured2 marks
Question 5(a)
5(a)
The Hall probe is now moved away from the wire, along the line XY . On the axes of Fig.5.2, sketch a graph to show the variation of the Hall voltage \(V_{\mathrm{H}}\) with distance x of the probe from the wire. Numerical values are not required on your sketch.
Mediumstructured2 marks
Answer
only curve with decreasing gradient acceptable value near x=0 and does not reach zero (if graph line less than 4.0 cm do not allow A1 mark) (no credit if graph line has positive and negative values of \(V_{\mathrm{H}}\) )
Question 7
7
Two long straight parallel copper wires A and B are clamped vertically. The wires pass through holes in a horizontal sheet of card PQRS, as shown in Fig. 7.1.
structured6 marks
Question 7(a)
7(a)
There is a current in wire A in the direction shown on Fig. 7.1. On Fig. 7.1, draw four field lines in the plane PQRS to represent the magnetic field due to the current in wire A.
Easystructured3 marks
Answer
sketch: concentric circles (minimum of 3 circles) M1 separation increasing with distance from wire A1 correct direction B1
Question 7(c)
7(c)
The direct currents in wires A and B are now replaced by sinusoidal alternating currents of equal peak values. The currents are in phase. Describe the variation, if any, of the force experienced by wire B.
Hardstructured3 marks
Answer
force always towards wire A/always in same direction varies from zero (to a maximum value) variation is sinusoidal / \(\sin ^{2}\) (at) twice frequency of current (any two, one each) 8
Question 6
6
8 marks
Question 6(b)
6(b)
A long air-cored solenoid is connected to a power supply, so that the solenoid creates a magnetic field. Fig. 6.1 shows a cross-section through the middle of the solenoid. The direction of the magnetic field at point W is indicated by the arrow. Three other points are labelled X, Y and Z .
structured5 marks
Question 6(b)(i)
6(b)(i)
On Fig. 6.1, draw arrows to indicate the direction of the magnetic field at each of the points X, Y and Z .
Mediumstructured3 marks
Answer
arrow from X pointing horizontally to the left B1 arrow from Y pointing diagonally upwards and to the left at about \(45^{\circ}\) B1 arrow from Z pointing horizontally to the right B1
Question 6(b)(ii)
6(b)(ii)
Compare the magnitude of the flux density of the magnetic field: - at X and at W - at Y and at Z .
Mediumstructured2 marks
Answer
(flux densities at W and X are approximately) equal B1 (flux density at) Y greater than (flux density at) Z B1
Question 6(c)
6(c)
Two long parallel current-carrying wires are placed near to each other in a vacuum. Explain why these wires exert a magnetic force on each other. You may draw a labelled diagram if you wish.
Mediumstructured3 marks
Answer
current in wire creates magnetic field around wire B1 (each) wire sits in the magnetic field created by the other B1 (for each wire,) current / wire is perpendicular to magnetic field (due to other wire), (so) experiences a (magnetic) force B1