Please Note: It may not always be possible to include the necessary special characters, superscripts, subscripts, etc. in e-mail responses to this group of exercises. We suggest that you discuss this matter with your professor/class and decide upon a system for indicating such characters. You may cut/paste some characters and/or Greek letters from Microsoft Word, using the Insert menu. Alternatively, we suggest that you agree upon abbreviations for or spell out symbols, Greek letters, or characters and indicate superscripts and subscripts by using "sup", "sub", or up/down carats.

m2 = m3 = 2.00 × 10-26 kg |q3| = |q4| = 3.00 × 10-16 C v2 = v3 = 1.00 × 106 m/s r2 = r4 = 10.0 cm B = 0.500 T

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Determine the following:

1			The particle(s) with no charge Need a Hint?
2			The particle(s) with positive charge Need a Hint?
3			The particle(s) with negative charge Need a Hint?
4			The central force on particle 2 Need a Hint?
5			The charge of particle 2 Need a Hint?
6			The radius of curvature for particle 3 Need a Hint?
7			The momentum of particle 4 Need a Hint?
8			The magnitude of the force on particle 3 Need a Hint?
9			The magnitude of the force on particle 2 Need a Hint?
10			The mass of particle 4 Need a Hint?

Singly charged positive ions traveling at various speeds are introduced into the experimental apparatus shown in the following figure. The ions are first accelerated by the electric field established by placing a potential difference V₁ across the vertical parallel plates. Next, they pass through the velocity selector. Finally, they enter a region where a magnetic field of 0.200 T exists.

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m = 5.80 × 10-26 kg -- mass of the ions

q = 1.60 × 10-19 C -- charge on the ions

V1 = 20.0 V -- potential difference across the vertical parallel plates

V2 = 750 V -- potential difference across the horizontal parallel plates in the velocity selector

S = 5.00 × 10-2 m -- separation of the plates in the velocity selector

B1 = 0.500 T -- magnetic field in the velocity selector

B2 = 0.200 T -- final magnetic field experienced by the ions

Determine the following:

11			Minimum speed of ions entering the velocity selector Need a Hint?
12			Speed of ions exiting the velocity selector Need a Hint?
13			Radius of curvature of the ions in the magnetic field B2 Need a Hint?
14			Radius of curvature of the ions if the potential difference across the plates in the velocity selector is doubled Need a Hint?
15			Radius of curvature of the ions if the magnetic field in the velocity selector is doubled Need a Hint?
16			Radius of curvature of the ions if the mass of the ions is doubled Need a Hint?

The following figure shows a 2.00 kg, 2.00 m long conductor in a 4.00 T magnetic field. The magnetic field is in the xz plane.

m = 2.00 kg L = 2.00 m B = 4.00 T θ = 53.0°

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17			Magnitude of the current needed in the conductor in order for the magnetic force to support the weight Need a Hint?
18			Direction of the current Need a Hint?

A square coil of wire is mounted in a uniform magnetic field as shown below.

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I = 5.0 A B = 2.0 T N = 100 turns

19			Direction of the force exerted on the right side (ab) of the coil. Need a Hint?
20			Magnitude of the force exerted on the right side (ab) of the coil. Need a Hint?
21			Magnitude of the torque on the coil due to the current in side ab of the coil Need a Hint?
22			Direction of the torque on the coil due to the current in side ab of the coil Need a Hint?
23			Direction of the force exerted on the left side (cd) of the coil. Need a Hint?
24			Magnitude of the force exerted on the left side (cd) of the coil. Need a Hint?
25			Magnitude of the torque on the coil due to the current in side cd of the coil Need a Hint?
26			Direction of the torque on the coil due to the current in side cd of the coil Need a Hint?
27			Total torque acting on the coil

The following figure shows two parallel current-carrying wires held rigidly in place by wire mounts.

I1 = 1.00 A I2 = 2.00 A I3 = 1.00 A d = 2.00 cm + = out of page - = into page

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28			Magnitude and direction of the magnetic field at position A Need a Hint?
29			Magnitude and direction of the magnetic field midway between the wires Need a Hint?
30			Distance from wire 1 to where B = 0 Need a Hint?
31			Magnitude and direction of the force per unit length on wire 1 Need a Hint?
32			What would need to be done to the current in wire 1 in order to get B = 0 at position A Need a Hint?