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# 9 Physics word problems: Magnitude of compass needle, magnet, magnetic field, alpha particle speed, current, coil, galvanometer, resistance

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1. A compass needle in a uniform magnetic field of 0.30 T experiences a torque of 0.050 N * m when it points in a direction 45 degrees away from the direction of the field. What is the magnitude of the needle's magnetic moment?

2. A slender, 150-g bar magnet 15.0 cm long has a magnetic moment of 5.30 x 10^6 A * m^2. It is held at an angle of 45 degrees to the direction of a uniform magnetic field. When released, it begins to rotate about its center with an intial angular acceleration of 5.09 x 10^-3 rad/s^2. What is the magnitude of the magnetic field.

3. A wire 0.250 m long carries a current of 0.750 A in a region of uniform magnetic field. The wire is subject to a force of 2.50N when held perpendicular to the direction of the field. What is the magnitude of the magnetic field?

4. Alpha particles from a particular radioactive source have a speed of 1.85 x 10^7 m/s. How large a magnetic field is required to bend the path of the particles into a circle of 0.580-m radius? An alpha particle has a mass of 6.64 x 10^-27 kg and a charge of 3.20 x 10^-19 C.

5. A long straight wire carries a current of 100mA. What is the magnitude of the magnetic field 10.0cm from the wire?

6. Two parallel wires spaced a distance d apart experience an attractive fore per unit length of 6.00 x 10^-4 N/m. If the currents have a magnitude of 10.0A each, what is the distance d?

7. A coil of 32 turns of wire is wound about a circular form. The average diameter of the individual loops is 28.5 cm. Calculate the magnetic moment of the coil when it carries a current of 1.75A.

8. A lab technician needs to make an ammeter that measures 15 A full scale. The only galvanometer available deflects full scale as a current of 100 microA, and its resistance is 10kOhm. What resistance is needed and how should it be connected to the galvanometer?

9. A student needs to make a voltmeter that measures 200V full scale. The only galvanometer available deflects full scale at a current of 10.0 mA, and its resistance is 1.00 kOhm. (a) What resistance is needed and how should it be connected to the galvanometer? (b) Draw a circuit diagram for the resulting meter.

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#### Solution Preview

See the attached file.

1.)
Torque T = M*B*sin(theta)
B = 0.30 T
torque = 0.050 N * m
theta = 45 degree
M = magnetic moment = T/(B*sin(45)) = 0.05/(0.3*sin(45))
=> M = 0.2357 A*m^2 --Answer

2.)
mass m = 150 g = 0.15 kg
length l = 15.0 cm = 0.15 m
magnetic moment M = 5.30 x 10^6 A * m^2
Angle with field theta = 45 degrees
angular acceleration alpha = 5.09 x 10^-3 rad/s^2
magnetic field B = ?

Torque = M*B*sin(theta) = I*alpha
I = moment of inertia = (1/12)*m*l^2
=> I = (1/12)*0.15*0.15^2 = 2.81*10^(-4) kg-m^2
Therefore,
5.30 * 10^6*B*sin(45) = 2.81*10^(-4)*5.09 * 10^(-3)
=> B = 14.3029*10^(-7)*sqrt(2)/(5.30 * 10^6)
=> B = 3.82*10^(-13) Tesla ...

#### Solution Summary

For each problem, the solution shows the formulas with explanations needed to solve the problem.

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