# 6 Physics problems: Calculating ion field paths

1. A singly charged positive ion has a mass of 2.5*10^-26kg. After being accelerated through a potential difference of 250V, the ion enter a magnetic field of 0.50T, in a direction perpendicular to the field. Find the radius of the path of the ion in the field.

2. Two ions with masses of 5.1*10^-26kg move out of the slit of a mass spectrometer and into a region in which the magnetic field is 0.04T. Each has a speed of 1.44*10^6m/s, but one ion is singly charged while the other is doubly charged. I. Find the radius of the circular path followed by each in the field, and II. the distance of separation when they have move through one half their circular path and strike a piece of photographic paper.

3. A swimmer is in a deep pool with her eyes a horizontal distance R=1.5m from the edge. How far below the surface are her eyes if she is just able to see the full height of a lifeguard who is standing on the pool's edge?? The index of refraction of water is 1.33.

4. A submarine is 314m horizontally out from the shore and 111m beneath the surface of the water. A laser beam is sent from the sub so that it strikes the surface of the water at a point 214m from the shore. If the beam just strkes the top of a building standing directly at the water's edge, find the height of the building.

5. The radius of the galaxy is 3*10^18m I. How fast would a spaceship have to travel to cross the entire galaxy in 441 years, as measured from within the spaceship?? II. How much time would elapse on Earth?

6. If it takes 3750MeV of work to accelerate a proton from rest to a speed of v, determine v.

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#### Solution Preview

1.) mass of ion (m) = 2.5*10^(-26) kg

charge (q) = 1.6 * 10^(-19) Coulomb (Because, singly ionised)

Potential difference (V) = 250 Volt

Magnetic field intensity (B) = 0.5 Tesla

Because ion is accelerated by a potential difference of V, therefore,

q*V = energy gained = kinetic energy = (1/2)m*v^2

=>v = sqrt(2*q*V/m) ............(1)

when ion eneters a magnetic field, perpendicular to the direction of field, because of charge and motion of the ion it will trace a circular path. The centripetal force is obtained from magnetic (Lorentz)force:

q*v*B = m*v^2/r

where r is the radius of circular path traced by ion.

=> q*B = m*v/r => r = m*v/(q*B)

substitute the value of v from equation (1), we get,

r = m*sqrt(2*q*V/m)/(q*B)

=> r = sqrt(2*m*V/q)/B

=> r = sqrt[2*2.5*10^(-26) * 250/{1.6*10^(-19)}]/0.5

=> r = sqrt[2*25*250*10^(-26+19)/16]/0.5

=> r = 2*sqrt(2*25*25*10^(-7+1)/16]

=> r = 2*5*5*10^(-3)*sqrt(2)/4

=> r = 12.5*sqrt(2)*10^(-3) meter

=> r = 17.67 *10^(-3) meter = 1.76 Cm Answer

2.) mass m1 = ...

#### Solution Summary

In very detailed solutions, the problems are explained and solved.

Physics: Magnetic & Induction

See attached document for questions.

Magnetics & Induction

4a1. Find the direction and magnitude of force exerted on an electron with initial velocity (= 100 m/s) along +x axis, if

o

the magnetic field (2 T) is pointing at +30

angle from +X axis, in the XY plane.

-19

Hint: F = (-1.6x10

C)(100 m/s)(2T)sin(30 ) = N, along the - z direction, i.e. into the paper.

4a2. Find the direction and magnitude of force exerted on an electron with initial velocity (= 1000 m/s) along +x axis,

if the magnetic field ( 2 T) is pointing in +z direction, i.e. out of the paper.

4b1. A proton with velocity ( 5x10

m/s) in +y direction, enters a region where B ( 0.1 T) is in +z direction. Calculate

the radius of resulting circular path. Use [5].

4b2. What must have been the accelerating voltage, if above mentioned proton motion were a part of the mass-

+

spectrometer described in Module4b? How strong a B is needed if the detected ion is charged iron (Fe ) instead? Use

[6], and then use [7].

4c1. A 2 m long wire conducting 10 A in +x direction, is placed in 0.1 T magnetic field pointing in +z direction. Calculate the magnitude and the direction of the force.

4c2. A square coil (A = 0.01 sq. m.) of 100 turns is placed horizontally, in a magnetic field ( 1 T) pointing towards right. Calculate the total force on the coil, if the current is 10 A.

4d1. A square coil (A = 0.01 sq. m.) of 100 turns is placed horizontally, in a magnetic field ( 1 T) pointing towards right. Calculate the torque on the coil, if the current is 10 A. Draw a diagram, and use [11].

4d2. Calculate the average torque on the coil as it turns through quarter turn, by taking average of a table of 10 values

o

of sin function at 10

interval. Set up an excel spreadsheet with a column with angles from 0o to 90o. If the arrangement

is turned into a DC motor, calculate the power if the rotor is spinning at 3600 RPM. (Hint: Poweraverage = average*)

4e1. Calculate the B field of a straight conductor carrying 10 A current at r = 0.01 m.

4e2. Two wires (each of length L = 1 m ) are placed , along +Z, parallel to each other at distance d= 0.1m. They carry current I1 = 10 A and I2 = 5 A respectively. See section 19.8 in Serway Text 7th edition.

Draw a diagram.

(1) Calculate the B the field at the location of wire 2 produced by the wire 1.

(2) Calculate the force on the wire 2 due to the B field produced by 1, calculated above. (3) Likewise calculate the force on the wire 1 due to the field produced by wire 2.

(4) What would happen if the direction of current in both wires were to be reversed?

(5) What would happen if the direction of current is reversed in only one wire?

(Continued.....)

4f1. A bar of 1 m length aligned in y direction moves in +x direction at 10 m/s, in space where B = 1 T pointing in the - z direction. Calculate the motional EMF.

4f2. If the bar, in 4f1 above, is a part of a circuit (shown in the diagram below) with a light bulb of 10 resistance, what would be the induced current?

I

Y

v

B

X

4f3. Show that the electrical power dissipated in the light bulb in 4f2 is equal to the mechanical power supplied by force which moves the bar.

(Hints: P = I2R. Calculate the magnetic force on the bar, then use P = Fv)

4g1. Verify equation [19] E = -/t , for the 4f2 above, i.e. calculate the rate of change of flux.

4g2. A square coil (A = 0.01 m ) of 100 turns is in the xz plane, where the B field of 10 T is pointing in the +x direction. Calculate average induced EMF if the coil is rotated by 10 degrees (about z axis) in 0.1 s. (An external agent rotates the coil, and EMF is produced: An example of Electrical Generator )

4h1. Consider a loop in xy plane, in magnetic field pointing in the -z direction. What would be the direction of the induced current if the original B field were decreasing?

4i1. Calculate the amplitude of the AC voltage generated by an electric generator if the shaft is rotating at 60 RPM, and A = 1 m , B = 1 T, N = 1000.

4i2. The coil of a AC motor has resistance of 4 . Assume that under operating condition the rms value of the back EMF produced is 118 V, when it is drawing power from 120 V wall outlet. Calculate the startup current, and the operating current.

4j1. A 100 turn solenoid's dimensions are: l = 0.2m, r = 0.025m. Calculate the L. {n = N/ l }

4j2. Calculate the induced voltage if the current through above solenoid is changing at the rate of 100 A/s.

4j3. Calculate the stored magnetic energy in the above solenoid if the current is 5 A at a given time.

4j4. Calculate mutual inductance between two coils if 50 A/s rate of change of current through one coil induces 2 volts across another coil.

4j5. (a) Explain why the transmission lines have high voltage.

(b) Explain why high voltage is not usually used near the point of use (i.e. home, industry).

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