Electromagnetic Induction
1.
A
7.
C
8.
C
9.
C
2.
D
3.
A
4.
D
5.
D
6.
C
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
1

16.
D
17.
A
18.
C
19.
B
10.
D
11.
C
12. (a) (i) M shown at peak or trough;
(ii) Z shown on t -axis;
(b) by Lenz’s law, emf (or current) must change direction as flux cutting changes direction; as magnet oscillates, flux is cut in opposite directions;
13.
B
14.
A
15.
D
[1]
[1]
1
1
2
[4]
[1]
[1]
2
[1]
[1]
[1]
[1]
[1]

20.
B
21.
A
22.
C
23.
B
24.
A
25.
(i) (induced) e.m.f. proportional to rate of change of magnetic flux (linkage);
(do not allow induced current) as current increases, magnetic field in coil increases; thus change in flux linkage and e.m.f. induced;
(ii) direction of (induced) e.m.f. such as to tend to oppose; the change producing it; induced e.m.f. must oppose e.m.f. of battery / growth of current in circuit;
(iii) energy is supplied by the battery; in making charge move against the induced e.m.f.;
26.
Electromagnetic induction
(a) the induced emf is induced in such a direction that its effect is to oppose the change to which it is due / OWTTE ;
(b) description : on opening the switch, the reading on the voltmeter will deflect to the left and then drop to zero; explanation: when the switch is opened the field drops to zero − so again a time changing flux; which will induce an emf in the opposite direction as the emf will now be such as to oppose the field falling to zero / Lenz’s law; when the current reaches zero, there will no longer be a flux change;
3
3
2
1
4
[1]
[1]
[1]
[1]
[1]
[8]
[5]
3

27.
(a) (i) emf (induced) proportional to; rate of change / cutting of (magnetic) flux (linkage);
(ii) magnetic field / flux through coil will change as the current changes;
(b) (i) sinusoidal and in phase with current;
(ii) sinusoidal and same frequency; with 90° phase difference to candidate’s graph for ϕ ;
(iii) emf is reduced; because B is smaller;
Award [0] for “emf is reduced” if argument fallacious.
(c) advantage: no direct contact with cable required; disadvantage: distance to wire must be fixed;
28.
(a) e.m.f. induced proportional to/equal to; rate of change of flux (linkage) / rate of flux cutting;
(b) (i) for e.m.f./current to be induced in secondary, flux must be changing in the core; changing flux is caused by varying current in primary;
(ii) induced currents in core are kept small; ( do not allow reduced/ prevented ) to reduce heating/energy losses;
( do not allow mere “eddy current losses” )
(iii) use of
N
S
N
P
=
V
V
S
P
; to give N
P
= 8600 turns; and I
P


=
42
230


= 180 mA;
29.
Electrical conduction and induced currents
(a) the force on the electrons produced by the electric field causes them to accelerate along the direction of the rod; however, they will (soon) collide with a lattice ion but after collision will again be accelerated (along the rod) before making another collision /
OWTTE ; hence the electrons gain a drift / net velocity in the direction of the wire / in the (opposite) direction to the field even though they still have random velocities / OWTTE ;
2
2
2
2
2
2
3
3
2
1
1
[10]
[9]
4

(b) (i)
1
(ii) Lenz’s law says that the direction of the induced current is such as to oppose change; therefore, to produce a (magnetic) force that opposes F the current must be in direction shown / reference to left / right hand rule / OWTTE ; 2
(iii) the force on the electrons is given by Bev ; as v increases so does this force and therefore, so does the induced current; therefore, net force on rod decreases / OWTTE ;
(c) (i) the induced emf is equal / proportional to the rate of change / cutting of
(magnetic) flux;
3
1
(ii) if the rod moves a distance ∆ x in time ∆ t then area swept out by rod = l ∆ x ; flux = Bl ∆ x; rate of change of flux =
Bl ∆ x
= Blv =
;
∆ t
(iii) induced current:
F
I = ;
Bl substitute to give I = 3.1A; speed v :
ε = IR = 0.47;
ε = Bvl substitute to give v = 4.5 (4.4) ms
− 1
;
3
4
1
1
30.
(a) (i) correct labelling of A and V;
(ii) P on resistor at “bottom”;
(b) (i) I = 0.40 A;
R =
V
I
=
10
0 .
40
= 25 Ω ;
(ii) the rate of increase of I decreases with increasing V / OWTTE; because: the conductor is (probably) heating up as the current increases / OWTTE ; and resistance (of a conductor) increases with increasing temperature;
(c) (i) from graph, current in Y = 0.30A; current in X = 0.20A to give total current = 0.50A;
(ii) potential across Z = 7.0V;
2
3
2
[17]
5

therefore, R =
7 .
0
0 .
50
= 14 Ω ;
(iii) resistance of parallel combination
14
7
× 5 or
5 .
0
0 .
50
;
= 10 Ω ; or resistance of Y =
5 .
0
0 .
30
= 17 Ω and resistance of X is 25 Ω ; so combination =
25 × 17
= 10 Ω ;
42
(d) (i) upwards the direction of the compass needle is the resultant of two fields
/ OWTTE ; the field must be into the plane of the (exam) paper to produce a resultant field in the direction shown / OWTTE ;
Award [1] for “upwards because of the right hand rule” / OWTTE.
(ii)
2
2
2 vector addition with correct values of two angles shown 30 ° , 60 ° or 90 ° ; from diagrams B
E
= B
W
× tan 60 or B
E
=
B
W tan 30
;
(e) (i) the emf induced in a circuit / coil / loop is equal to / proportional to; the rate of change of flux linking the circuit / coil / loop;
Do not allow “induced current”.
(ii) the induced emf / current is in such a direction that its effect is to oppose the change to which it is due / OWTTE ;
(f) (i) description: on closing the switch, the reading of the voltmeter will increase to a maximum value; then drop back to zero; explanation: on closing the switch, a magnetic field is established in the solenoid so a flux links the loops; the field is changing with time / the current is changing with time so an emf is induced in the loops; when the current reaches a maximum there is no longer a time changing flux so there is no induced emf;
(ii) description: on opening the switch, the reading on the voltmeter will increase to a maximum value but in the opposite direction; and then drop to zero; explanation:
2
2
1
4
6

when the switch is opened the field drops to zero − so again a time changing flux which will induce an emf in the opposite direction as the emf will now be such as to oppose the field falling to zero
/ Lenz’s law; when the current reaches zero, there will no longer be a flux change;
31.
Electromagnetic induction
(a) (i) 3.3 × 10
− 2
T;
(ii) flux linkage = 3.3 × 10
− 2
× 1.7 × 10
− 4
× 250;
= 1.4 × 10
− 3
Wb (turns);
Award [0] if answer given as flux in (a)(ii) but allow full credit in (b)(i).
(b) (i) new flux linkage = 7.23 × 10
− 4
Wb turns or ∆ B = 1.6 × 10
− 2
T; change = (1.4 − 0.7) × 10
− 3 or change = 1.6 × 10
− 2
× 1.7 × 10
− 4
× 250; change = 7 × 10
− 4
Wb turns (no mark for answer)
(ii) e.m.f.
is proportion al/equal to rate of
(linkage); change of flux 


(do not al low
"induced c urrent" ) emf =
(
7 × 10
− 4
)
=
0 .
35
2 × 10
− 3
V ;
(c) (i) emf / induced current acts in such a direction to (produce effects to) oppose the change causing it;
(ii) induced current produces a magnetic field in the coil / induced current is in field of magnet; this produces a force; (award only if the first marking point is correct) the force acts to oppose the motion of the coil;
4
1
2
2
2
1
3
[28]
[11]
7