Question
I havetwo problems that are a bit confusing to me. Any help is greatlyappreciated. Thanks! A long straight wire carries a current of 2.20A in thedirection shown below. A helium nucleus moves toward the wire witha speed of 2.65 E6 m/s. At the instant shown, the helium nucleus is1.00m away from the wire. Find the force (magnitude and direction)on the helium nucleus due to the current in the wire. Also asimiliar problem: A transformer has 6.00 E4 turns in its primary coil and 3.00E3 turns in its secondary coil. The primary coil is supplied withan alternating current at an rms voltage of 220.0 v. The rmscurrent in the secondary coil is 5.00 A. Find: a) the rms voltage across the secondary coil- b) the rms current in the primary circuit- c) the power in each circuit- I havetwo problems that are a bit confusing to me. Any help is greatlyappreciated. Thanks! A long straight wire carries a current of 2.20A in thedirection shown below. A helium nucleus moves toward the wire witha speed of 2.65 E6 m/s. At the instant shown, the helium nucleus is1.00m away from the wire. Find the force (magnitude and direction)on the helium nucleus due to the current in the wire. Also asimiliar problem: A transformer has 6.00 E4 turns in its primary coil and 3.00E3 turns in its secondary coil. The primary coil is supplied withan alternating current at an rms voltage of 220.0 v. The rmscurrent in the secondary coil is 5.00 A. Find: a) the rms voltage across the secondary coil- b) the rms current in the primary circuit- c) the power in each circuit-
Explanation / Answer
1)the kinetic energy of the helium nucleus is equal to thework done to bring the helium nucleus at a distance 1.00 m awayfrom the wire therefore W = K or F * d = (1/2)m * v^2 or F = (1/d) * (1/2)m * v^2 d = 1.00 m,m = 4 g/mol = 4 * 10^-3 * 0.012 kg = 48 * 10^-6 kgand v = 2.65 * 10^6 m/s 2)a)we know that (Vs/Vp) = (Ns/Np) or Vs = (Ns/Np) * Vp Ns = 3.00 * 10^3 turns Np = 6.00 * 10^4 turns Vp = 220.0 V(rms) b)the rms current in the primary circuit (Ip/Is) = (Ns/Np) or Ip = (Ns/Np) * Is Is = 5.00 A(rms) c)the power in each circuit Pp = Vp * Ip (inputpower) Vp = 2 * Vrms = 2 * 220.0V Ip = 2 * Irms = 2 *5.0 or Pp = 2 * Vrms *Irms similarly,the power in the output Po = Vo * Io = 2 *Vs * Is