Concept explainers
The radius of the alpha particle’s trajectory.
Answer to Problem 63AP
The radius of the alpha particle’s trajectory is
Explanation of Solution
Write the equation for the radius of the trajectory of the proton.
Here,
Write the equation for the radius of the trajectory of the alpha particle.
Here,
Write the equation for the principle of conservation of linear momentum.
The alpha particle's mass is four times the proton's mass.
Substitute
Write the equation for the principle of conservation of energy.
Substitute
Take the square of equation (IV) and then divide by
Compare the equation (VI) and (VII).
Rewrite the equation (I).
Rewrite the equation (II).
Substitute
The alpha particle's charge is twice the proton's charge.
Substitute
Conclusion:
Therefore, the radius of the alpha particle’s trajectory is
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Chapter 29 Solutions
Physics: for Science.. With Modern. -Update (Looseleaf)
- A circular coil 15.0 cm in radius and composed of 145 tightly wound turns carries a current of 2.50 A in the counterclockwise direction, where the plane of the coil makes an angle of 15.0 with the y axis (Fig. P30.73). The coil is free to rotate about the z axis and is placed in a region with a uniform magnetic field given by B=1.35jT. a. What is the magnitude of the magnetic torque on the coil? b. In what direction will the coil rotate? FIGURE P30.73arrow_forwardWithin the green dashed circle shown in Figure P23.28, the magnetic field changes with time according to the expression B = 2.00t3 − 4.00t2 + 0.800, where B is in teslas, t is in seconds, and R = 2.50 cm. When t = 2.00 s, calculate (a) the magnitude and (b) the direction of the force exerted on an electron located at point P1, which is at a distance r1 = 5.00 cm from the center of the circular field region. (c) At what instant is this force equal to zero?arrow_forwardA wire carrying a current I is bent into the shape of an exponential spiral, r = e, from = 0 to = 2 as suggested in Figure P29.47. To complete a loop, the ends of the spiral are connected by a straight wire along the x axis. (a) The angle between a radial line and its tangent line at any point on a curve r = f() is related to the function by tan=rdr/d Use this fact to show that = /4. (b) Find the magnetic field at the origin. Figure P29.47arrow_forward
- A magnetic field exerts a torque on each of the current carrying single loops of wire shown in Figure OQ22.12. The loops lie in the xy plane, each carrying the same magnitude current, and the uniform magnetic field points in the positive x direction. Rank the loops by the magnitude of the torque exerted on them by the field from largest to smallest Figure OQ22.12arrow_forwardTwo long, straight, parallel wires carry currents that are directed perpendicular to the page as shown in Figure P30.9. Wire 1 carries a current I1, into the page (in the negative z direction) and passes through the x axis at x = +. Wire 2 passes through the x axis at x = 2a and carries an unknown current I2. The total magnetic field at the origin due to the current-carrying wires has the magnitude 20I1(2a). The current I2 can have either of two possible values, (a) Find the value of with the smaller magnitude, stating it in terms of I1, and giving its direction. (b) Find the other possible value of I2.arrow_forwardA proton (charge + e, mass mp), a deuteron (charge + e, mass 2mp), and an alpha particle (charge +2e, mass 4mp) are accelerated from rest through a common potential difference V. Each of the particles enters a uniform magnetic field B, with its velocity in a direction perpendicular to B. The proton moves in a circular path of radius rp. In terms of rp, determine (a) the radius rd of the circular orbit for the deuteron and (b) the radius ra for the alpha particle.arrow_forward
- A proton moving in the plane of the page has a kinetic energy of 6.00 MeV. A magnetic field of magnitude H = 1.00 T is directed into the page. The proton enters the magnetic field with its velocity vector at an angle = 45.0 to the linear boundary of' the field as shown in Figure P29.80. (a) Find x, the distance from the point of entry to where the proton will leave the field. (b) Determine . the angle between the boundary and the protons velocity vector as it leaves the field.arrow_forwardWithin the green dashed circle show in Figure P30.21, the magnetic field changes with time according to the expression B = 2.00t3 4.00t2 + 0.800, where B is in teslas, t is in seconds, and R = 2.50 cm. When t = 2.00 s, calculate (a) the magnitude and (b) the direction of the force exerted on an electron located at point P, which is at a distance r = 5.00 cm from the center of the circular field region. (c) At what instant is this force equal to zero? Figure P30.21arrow_forward
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