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1. A proton of charge + 1.6 x 10^(-19) C and mass 1.67 x 10(-27)kg is introduced into a region of B = 1.5 T with an initial velocity of 1.25 x 10^6 m/s perpendicular to B. What is the radius of the proton's path?

2. A coil 17 cm in diameter and wound with 12 turns of wire is placed with the plane of the coil at right angles to a magnetic field of .038 T. What emf is induced in the coil if the field is halved in 0.54s. ?

3. A capacitor C = 4.7 nF is connected across a 2.5 mH inductor. What is the natural oscillation frequency of the combination?

4.What is the critical angle for a glass-to-water interface? Assume a refractive index of 1.50 for the glass?

5. A coin 2.0 cm in diameter is held 20 cm from a concave spherical mirror of 30 cm radius of curvature. Locate the image of the coin and its height?

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Solution Preview

1. A proton of charge + 1.6 x 10^(-19) C and mass 1.67 x 10^(-27)kg is introduced into a region of B = 1.5 T with an initial velocity of 1.25 x 10^6 m/s perpendicular to B. What is the radius of the proton's path?

Force on proton = F= q v B sin theta
where theta is the angle between the velocity and the direction of the magnetic field
in this case theta = 90 degrees therefore Sin theta = 1

Therefore Force on proton = F= q v B sin theta = q v B x 1 = qvB

This force provides the centripetal force= m v ^2 / r
Equating the two
mv^2/r = qvB
or r= mv/ qB

m= 1.67 x 10^(-27) kg
v= 1.25 x 10^6 m/s
B= 1.5 T
q= 1.6 x 10^(-19) C

Therefore r= mv/ qB = 0.0087 m