1.
A
[1]
2.
C
[1]
3.
C
[1]
4.
D
[1]
5.
A
[1]
6.
D
[1]
7.
B
[1]
8.
D
[1]
9.
A
[1]
10.
A
[1]
1
11.
B
[1]
12.
C
[1]
13.
D
[1]
14.
A
[1]
15.
(a)
(b)
(i)
M shown at peak or trough;
1
(ii)
Z shown on t-axis;
1
by Lenz’s law, emf (or current) must change direction as flux cutting
changes direction;
as magnet oscillates, flux is cut in opposite directions;
2
[4]
16.
Electromagnetic induction
(a)
(b)
the induced emf is induced in such a direction that its effect is to oppose
the change to which it is due / OWTTE;
1
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;
4
[5]
2
17.
(i)
(induced) e.m.f. proportional to rate of change of magnetic flux (linkage);
(do not allow induced current)
(ii)
(iii)
as current increases, magnetic field in coil increases;
thus change in flux linkage and e.m.f. induced;
3
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;
3
energy is supplied by the battery;
in making charge move against the induced e.m.f.;
2
[8]
18.
(a)
(b)
(i)
emf (induced) proportional to;
rate of change / cutting of (magnetic) flux (linkage);
2
(ii)
magnetic field / flux through coil will change as the current changes;
1
(i)
sinusoidal and in phase with current;
1
(ii)
sinusoidal and same frequency;
with 90° phase difference to candidate’s graph for ϕ;
2
emf is reduced;
because B is smaller;
2
(iii)
Award [0] for “emf is reduced” if argument fallacious.
(c)
advantage: no direct contact with cable required;
disadvantage: distance to wire must be fixed;
2
[10]
19.
Electromagnetic induction
(a)
(i)
3.3 × 10−2 T;
(ii)
flux linkage = 3.3 × 10−2 × 1.7 × 10−4 × 250;
= 1.4 × 10−3Wb (turns);
1
2
Award [0] if answer given as flux in (a)(ii) but allow full credit in (b)(i).
3
(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;
2
change = 7 × 10−4Wb turns (no mark for answer)
(ii)
e.m.f. is proportion al/equal to rate of change of flux  (do not allow

(linkage);
"induced current" )
(7 ×10 ) = 2 ×10
−4
emf =
(c)
(i)
(ii)
0.35
−3
2
V;
emf / induced current acts in such a direction to (produce effects to)
oppose the change causing it;
1
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;
3
[11]
20.
(a)
(b)
force exerted per unit mass;
on a small / point mass;
from the law of gravitation, the field strength
2
F
M
=G 2 ;
m
R
= g0 to give GM = g0R2;
NB To achieve full marks, candidates need to state that
2
F
=
m
g0.
(c)
downwards; (accept 90° to B field or down the wire)
1
(d)
F = Bevcosθ;
1
4
(e)
work done in moving an electron the length of the wire is
W = FL = BevLcosθ;
emf = work done per unit charge;
therefore, E = BLvcosθ;
or
F
electric field =
= Bvcosθ;
e
emf E = electric field × L;
to give E = BLvcosθ;
3
Award [2 max] if flux linkage argument is used.
(f)
F=G
Mm mv 2
=
;
r
r2
such that v2 =
(g)
GM g 0 R 2
;
=
r
r
v2 =
10 × (6.4) 2 × 1012
to give v = 7.8 × 103 m s–1;
6
6.7 × 10
L=
E
;
Bv cos θ
=
10 3
=2.2 × 104 m;
6.3 × 10 −6 × 7.8 × 10 3 × 0.93
3
2
[14]
21.
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;
3
5
(b)
(i)
1
(ii)
(iii)
(c)
(i)
(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
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;
3
the induced emf is equal / proportional to the rate of change / cutting of
(magnetic) flux;
1
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 =
(iii)
Bl∆x
= Blv = ε ;
∆t
3
induced current:
I=
F
;
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;
4
[17]
6