In the figure the ideal batteries have emfs E_1 = 11.0 V and E_2 = 0.500 E_1 and

Question

In the figure the ideal batteries have emfs E_1 = 11.0 V and E_2 = 0.500 E_1 and the resistances are each 4.66 ohm. What is the value of current in (a) resistor 2 and (b) resistor 3? A proton is accelerated from rest through 0.50 kV. It then enters a uniform magnetic field of 0.30 T that is oriented perpendicular to its direction of motion. What is the radius of the path the proton follows in the magnetic field? How long does it take the proton to make one complete circle in the magnetic field. The flexible loop in the figure below has a radius of 13 cm and is in a magnetic field of strength 0.20 T. The loop is grasped at points A and B and stretched until its area nearly zero. If it takes 0.25 s to close the loop, what is the magnitude of the average induced emf in it during this time? If the loop has a total resistance 50.0 ohm, what is the average induced current? What is the direction of the induced current? A laser beam is incident at an angle of 29.0 degree to the vertical onto a solution of corn

Explanation / Answer

6) Apply KVL to the left loop

-i1*R1-i3*R3+e1 = 0

4.66*i1 + 4.66*i3 = 11 .............(1)

Apply KVL to the right loop

(i2*R2)-e2+i3*R3 =0

(4.66*i2)+(4.66*i3) = 0.5*11..........(2)

apply KCL at the junction

i1+i2-i3 = 0 ................(3)

Solving (1) ,(2) and (3) we get

i1 = 1.18 A

i2 = 0 A is current through the resistor 2

i3 = 1.18 A is current through the resistor 3

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7) radius of the path is r = (m*v)/(q*B)

work doen by the potential differecne is W = q*dV = 0.5*m*v^2

1.6*10^-19*0.5*1000 = 0.5*1.67*10^-27*v^2

speed v is 3.1*10^5 m/sec

radius r = (m*v)/(q*B) = (1.67*10^-27*3.1*10^5)/(1.6*10^-19*0.3)

r = 0.01078 m = 1.07 cm

b) T = 2*pi*r/v = (2*3.142*0.01078)/(3.1*10^5) = 2.18*10^-7 sec

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8) a) induced emf e = B*dA/dt = 0.2*(3.142*0.13^2)/0.25 = 0.0424 V

B) induced current is V/R = 0.0424/50 = 0.000848 A = 8.48*10^-4 A

c) clock wise direction

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