Force on moving charge in magnetic and electric fields
- An electron (mass 9×10^-31 kg and charge 1.6×10^-19C) moving with speed c/100 (c = speed of light) is injected into a magnetic field B of magnitude 9×10^-4 T perpendicular to its direction of motion. We wish to apply an uniform electric field E toget… Answer: 2. vec E is perpendicular to vec B and its magnitude is 27×10² V m ⁻¹ Key idea: for the electron to go undeflected, the electric for... 1
- In the productF = q(v×B) = q v×(Bi+Bj+B_0k)For q = 1 and v = 2i+4j+6k and F = 4i-20j+12kWhat will be the complete expression for B ? Answer: 2. -6i-6j-8k Key idea: expand vec v×vec B as a determinant and match components. Here vec v=(2,4,6) , vec B=(B_x,B_y,B_z) , vec F=(4... 1
- An infinitely long straight conductor carries a current of 5 A as shown. An electron is moving with a speed of 10^5 m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the… Answer: 4. 8×10⁻²⁰ N Key idea: the electron moves parallel to the wire, so vec v⊥vec B and F=evB . B=μ₀I/2π r=dfrac2×10⁻⁷×50.2=5×10⁻⁶\ mathr... 1
- Ionized hydrogen atoms and α-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths r_H : r_α will be : Answer: 1. 2 : 1 In a magnetic field a charged particle moves in a circle of radius r=p/qB . Momentum p and B are the same, so r∝ 1/q . Ioni... 1
- An electron is moving in a circular path under the influence of a transverse magnetic field of 3.57×10^-2 T. If the value of e/m is 1.76×10^11 C/kg, the frequency of revolution of the electron is Answer: 4. 1 GHz An electron in a magnetic field circles with frequency f=eB/2π m=1/2π·e/m· B . f=frac1.76×10¹¹×3.57×10⁻²2×3.14=frac6.28×10⁹... 1