Download Exercises 1.

1. A small charged particle is moving in the presence of uniform magnetic and electric field with
constant velocity on a straight line. The velocity vector of the particle is ~v = (100m/s, 0, 0) and
~ = (0, 1T, 0). Give the direction and magnitude of the electric field!
the magnetic field vector is B
2. A small charged particle is moving in the presence of uniform magnetic and electric field with
constant velocity on a straight line. The velocity vector of the particle is ~v = (100m/s, 0, 0) and
~ = (0, 300N/C, 0). Give the magnetic field vector if its magnitude is
the electric field vector is E
B = 5T !
~ = (0.3T, 0.4T, 0)
3. A small charged particle is moving in the presence of uniform magnetic field of B
with constant velocity of ~v = (0, 6 m/s, 8 m/s) on a straight line. The mass and the charge of the
particle are m = 10−4 kg and Q = 10−4 C, respectively.
a.) Give the electric field vector !
b.) Give the angular velocity of the particle!
c.) Find the radius of the motion!
4. Find the force and the torque on the following current loops! The applied magnetic field of B = 1 T
is vertically downward directed in each cases. The current in the loops is I = 10 A.
a = 0.2m
a,
b,
c,
I
d,
I
I
b = 0.3m
I
b = 0.3m
5. Give the force on the wire below carrying a current of I = 10 A in the presence of uniform magnetic
field. The magnitude of the magnetic field is B = 1 T and its direction is indicated in the figure.
α = 30◦
B
a = 0.2m
α
I
6. Find the magnetic field at the center of the current loop! Apply the Biot–Savart law!
I
= 10 A
r
= 0.1 m
I
r
7. There are two long parallel straight wire carrying a currents of I1 = 10 A and I2 = 20 A, respectively.
The separation between them is d = 0.2 m. Find the force on a 1 m segment of the second wire if
the currents are parallel! How will change the force if the direction of I2 is reversed?
8. There are two long parallel wires lying on the table carrying a current of I 1 = 10 A and I2 = 20 A,
respectively. The currents are parallel in the wires. Where should we place a third wire so that the
force is zero on it?
1
I1
9. There are three long parallel wires as
it is shown by the figure. There is no
force on any of the wires. Give the currents in the second and the third wires
if I1 = 10 A, a = 0.1 m and b = 0.15 m.
I2
a
I3
b
10. There are three parallel wires intersecting the vertices of an equilateral triangle. Find the forces on
a l = 1 m segment of the wires!
a
a
a
I1
I2
I3
a = 0.1 m
I1 = 10 A
I2
I3
= 15 A
= 20 A
11. A circular current loop is connected to a long straight wire as it is shown by the figure. Find the
magnetic field at the center of the circle!
r
d
r
= 0.15 m
= 0.1 m
I
= 15 A
d
= 0.15 m
r
= 0.1 m
I
= 15 A
d
I
12. Find the magnetic field at the center of the circle!
I
r
2
13. Find the magnetic field at the center of the circle! Be carefull! The resistance for the longer part
of the circle is larger than the resistance of the shorter part! I = 10 A, r = 0.1 m.
I1
I
r
I2
I
14. Find the magnetic field at point A,B and C in Fig a.) and in Fig. b.)!
a = 0.2cm b = 0.15 m c = 0.1 m d = 0.1 m I = 10 A
a.)
d
2
d
2
B
C
A I
a
I
b
b.)
d
2
d
d
2
B
A
c
C
I
a
d
I
c
b
15. There are two long parallel straight line as it is shown by the figure. A square like current loop is
between the wires perpendicular to the plane of the wires. Find the force and the torque on the
current loop!
Side view
d
d
I1
a
d = 0.08 m
I1
I
I
a = 0.12 m
I = 15 A
= 12 A
d
d
Top view
a
16. There are a long straight wire carrying a current of I1 = 10 A and a rectangular loop of current
I2 = 15 A in the same plane.
3
d
a.) Find the force and the torque on
the current loop!
b
a
a = 0.1 m b = 0.2 m d = 0.1 m I1 = 10 A I2 = 10 A
I1
b.) Find the force on the wire if I2 is
unknown and the torque on the
loop is T = 10−4 N m
I2
a = 0.1 m b = 0.2 m d = 0.1 m I1 = 10 A
17. Find the torque on the frame between the solenoids.
l
I1
l
= 25 A
a
l = 0.2 m
a = 0.03 m
n = 100
I
I
1
1
18. We are going to make a solenoid from a wire which has a diameter of d = 1 mm. The current
through the solenoid will be I = 30 A. How large will the magnetic field be inside the solenoid?
4