Question Sheet 4 mproton = 1.67 x 10-27 kg

1. A long straight wire of radius R carries a steady current Io that is uniformly distributed through the cross section of the wire. (i) Sketch the magnetic field, B, around the wire if the wire is coming out of the page or going into the page. Make sure to show the direction of the B field. (ii) Derive a formula for the magnetic field strength at a distance r from the center of the wire for r > R? (iii) for r < R?

2. Two long parallel conductors each carry a current I = 10 A upwards. What is the magnitude and direction of the magnetic field at the midpoint of the line between them if the distance between them is 0.4 m (zero)

3. Two long parallel conductors carry currents I1 = 3.00 A and I2 = 3.00 A as shown above, both directed into the page. Determine the magnitude and direction of the resultant magnetic field at P.

4. Two long parallel wires, a distance 2d apart carry equal currents I in opposite directions (see diagram). If x is a distance measured from the midpoint between the two wires, show that for P located at (i) x < d (to right) the

magnitude of B is given by and it is directed downward (ii) x > d (to right) the

magnitude of B is given by and it is directed upward.

5. Two semicircular arcs having radii R1 = 3.15 cm & R2 = 7.80 cm form a loop, with a common center of curvature, C, and carrying a current I = 0.281 A as shown. Calculate the magnitude and direction of the net B at C. (1.67 µT, into paper)

6. Consider a rectangle PQRS of length 2.0 m and width 1.0 m as shown. There are 3 long straight wires at P, Q and R carrying currents 1.0 A, 5.0 A and 2.0 A respectively.

Calculate the net magnetic field at S. (6 x 10-7 T, downwards)

7. Directions of i1 and i2 currents are opposite as shown. If the magnetic field at the center of the circles is zero find the ratio of i1 to i2 i1/i2? (2/3)

x12 cm

P

5 cm

x

xx P

d.

d

C

x

Q

R

.P

.S

2 m1m

8. Find the magnetic field produced by currents i1 and i2 at point O. (4 x 10-6 T)

9. Find the magnetic field produced by the solenoid if the number of loop is 400 and current passing through on it is 5 A. Length of the solenoid is 40cm. (6 x 10-3 T)

10. A proton moves with a speed of 8.0 x 106 m/s along the x-axis. It enters a region where the magnetic field is of magnitude 2.5T, directed at 60o to the x-axis and in the xy plane. (i) Calculate the magnetic force (magnitude and direction) and the acceleration of the proton. (ii) Which of your answers would change if the particle were an electron? (2.8 x 10-12 N, out of paper, 1.7 x 1015 m/s2, direction and acceleration).

11. A particle (electron or proton) moves along a circle in a region of uniform B = 4.00 mT. It experiences a force of magnitude 3.20 x 10-15 N. Determine (i) what kind of particle it is (ii) its speed (iii) its radius (iv) its period. (electron, 5 x 10 6 m/s, 7.12 mm, 8.95 ns)

12. A proton moves with a velocity of v = (2i – 4j = k) m/s in a region in which the magnetic field is B = (i + 2j – 3k) T. What is the magnetic force this charge experiences? (2.34 x 10-18N)

13. A particle of charge q moves in a circle of radius r in a uniform magnetic field B. Show that its momentum is p=qBr.

14. Let the particle be a proton which moves in a circular path perpendicular to a 1.15 T magnetic field. The radius of its path is 8.4 mm. Calculate the kinetic energy of the proton in eV. (4469 eV).

15. Consider a wire of length 20 cm carrying a current of 2 A. It is placed perpendicular to a magnetic field going into the paper of uniform strength 0.15 T. (The wire lies in the + x direction). What are the magnitude and direction of the force on the wire? (0.060 N, upward).

16. A wire carries a steady current of 2.4 A. A straight section of the wire is 0.75 m long and lies along the x axis within a uniform magnetic field B = (1.6k) T. If the current is in the + x direction, what is the magnetic force on the section of the wire? (-2.88 j) N

17. For Question 6, calculate the force per unit length experienced by the wire at Q due to the currents in the other two wires. (2.1 x 10-6 N/m).

18. The diagram shows a long straight wire carrying a current of 50A. A rectangular loop carrying current of 20 A is placed with its long side parallel to the long wire, a distance of 10cm as shown. Determine (a) the magnitude and direction of B along QR due to the long wire. Hence find the magnitude and direction of the force on QR. (b) Obtain the magnitude and direction of the force on PQ. (40μT, 240 μN to the right, 183 µN upwards)

Q

R

20 A

P

50 A

1m

15 cm

10 cm

30 cm