586
13 Electromagnetism I
varies in time according to B = B 0 cos(15t). Calculate the electromotive
force induced in the coil.
[University of Manchester 2007]
13.17 A water droplet of radius 1 μm is charged such that the electric field on its
surface is 5.8 mV/m. (a) How many electrons does the droplet carry? (b) How
strong a vertical electric field is required to prevent it from falling?
13.18 An electron of energy 1 eV enters an infinitely large region containing only a
homogeneous magnetic field of 10 −3 T, at an angle of 60 ◦ to the direction of
the field. Calculate its subsequent motion assuming no energy losses. What
type of energy losses will occur even in complete vacuum?
[University of Manchester 1972]
13.19 A uniform electric field is established between the plates of a parallel plate
capacitor by holding one plate at ground and the other at a positive potential
V as shown. A uniform magnetic field B is established perpendicular to the
electric field (Fig. 13.2).
A charge −q is released from rest from the lower plate.
(i) Write down the equations of motion for the velocity components of the
charge.
(ii) Show that, at some time t later, the velocity of the electron in the xdirection is related to the distance y moved along the y-axis by
v x = ωy
(iii) By applying the conservation of energy or otherwise to determine the
square of the velocity in the x–y-plane, show that
v
2
y =
2qv
md
y − ω
2 y
2
[University of Aberystwyth, Wales]
Fig. 13.2
13 Electromagnetism I
varies in time according to B = B 0 cos(15t). Calculate the electromotive
force induced in the coil.
[University of Manchester 2007]
13.17 A water droplet of radius 1 μm is charged such that the electric field on its
surface is 5.8 mV/m. (a) How many electrons does the droplet carry? (b) How
strong a vertical electric field is required to prevent it from falling?
13.18 An electron of energy 1 eV enters an infinitely large region containing only a
homogeneous magnetic field of 10 −3 T, at an angle of 60 ◦ to the direction of
the field. Calculate its subsequent motion assuming no energy losses. What
type of energy losses will occur even in complete vacuum?
[University of Manchester 1972]
13.19 A uniform electric field is established between the plates of a parallel plate
capacitor by holding one plate at ground and the other at a positive potential
V as shown. A uniform magnetic field B is established perpendicular to the
electric field (Fig. 13.2).
A charge −q is released from rest from the lower plate.
(i) Write down the equations of motion for the velocity components of the
charge.
(ii) Show that, at some time t later, the velocity of the electron in the xdirection is related to the distance y moved along the y-axis by
v x = ωy
(iii) By applying the conservation of energy or otherwise to determine the
square of the velocity in the x–y-plane, show that
v
2
y =
2qv
md
y − ω
2 y
2
[University of Aberystwyth, Wales]
Fig. 13.2