Physics tutorial #17

1. (Cyclotron Frequency) A particle having charge q and mass m moves in a constant magnetic field ~

B

with initial velocity ~

v. Find the radius of the particle’s orbit and angular frequency if ~

v ⊥ ~

B and

v  c.

2. Electrons travel through a uniform magnetic field

at right angles to the field and traverse complete
circle in 10

−9

s. What is the magnitude of the

magnetic field?
(m

e

= 9.1 × 10

−31

kg, e = 1.6 × 10

−19

C)

B

e

3. Find the velocity v of electrons travelling along a straight line across the area with uniform electric

and magnetic fields if we know that ~

v ⊥ ~

E, ~

v ⊥ ~

B and ~

E ⊥ ~

B (values of E and B are known).

4. Two isotopes of uranium,

235

U (atomic mass

3.90 × 10

−25

kg) and

238

U (atomic mass 3.95 ×

10

−25

kg), are sent into a mass spectrometer with

a speed of 1.05 × 10

5

m/s, as indicated in the ac-

companying sketch.

Given that each each iso-

tope is singly ionised, and that the strength of
the magnetic field is 0.75 T, what is the distance
d between the two isotopes after they complete
half a circular orbit?

B

v

d

5. A copper rod 15 cm long and with a mass of 50 g is

suspended from two thin, flexible wires, as shown
in the figure. At right angles to the rod is a uni-
form magnetic field of 0.55 T. Find the direction
and magnitude of the electric current needed to
levitate the copper rod.

B

I

I

6. A circular coil 0.05 m in radius, with 30 turns of wire, lies in a horizontal plane. It carries a current

of 5 A in a counter-clockwise sense when viewed from above. The coil is in a uniform magnetic field
directed toward the right, with magnitude 1.2 T. (a) Find the magnitudes of the magnetic moment
and the torque on the coil. (b) If the coil rotates from its initial position to a position where its
magnetic moment is parallel to ~

B, what is the change in potential energy?

7. Use the law of Biot and Savart to show that the magnetic field near a long, straight, current-carrying

conductor is equal

B =

µ

0

I

2πr

Hint :

Z

xdy

(x

2

+ y

2

)

3/2

=

y

x

√

x

2

+ y

2

+ constant

!

.

8. (a) A long, straight wire carries a current of 7.5 A. How far from this wire is the magnetic field it

produces equal to the Earth’s magnetic field, which is approximately 5.0 × 10

−5

T ? (b) What value

of current would cause the magnetic field of 1 T in that distance?

Nivas Babu Selvaraj, Maciej Wo loszyn
http://fatcat.ftj.agh.edu.pl/~woloszyn/phys/