(a)
When a positively charged conductor is placed near a candle flame, the flame spreads out as shown in the diagram above. Explain this observation.
(b) A proton moving with a speed of 5.0 x 10(^{5}) ms(^{-1}) enters a magnetic field of flux density 0.2 T at an angle of 30° to the field. Calculate the magnitude of the magnetic fcrce exerted on the proton. [Proton charge = 1.6 x 10(^{-19}) C]
(c)
The diagram above illustrates a 9.0 V battery of internal resistance 0.5 (Omega) connected to two resistors of values 2.0 (Omega) and R (Omega). A(_1) A(_2) and A(_3) are ammeters of negligible internal resistances. If Al reads 4.0 A, calculate the:
(i) equivalent resistance of the combined resistors 2.0 (Omega) and R (Omega);
(ii) currents through A(_1) and A(_3) ; (iii) value of R.
Explanation
(a) The positively charged conductor attracts the negative charges in the air and repels the positive charges i.e. the candle flame ionizes the air around it.
= 1.6 x 10(^{-19}) X 5.0 X 10(^5) x 0.2 x Sin 30°
= 0.8 x 10(^{-1})
(c)(i)E = I (Rc + r)
9 = 4(Rc + 0.5)
R: = 9/4-0.5
= 1.75Ω
(ii) Lost volt = Ir = 4.0 x 0.5 =2.0 V
V oltage across 2Ω and RΩ
V = 9.0 – 2.0 = 7.0V
Current in A(_2) = I(_2) = (frac{2}{VR}) = 7/2 = 3.5A
Current in A(_3) = I(_3) = V/R = 7/14 = 0.5A
OR
A(_3) = A(_1) – A(_2)
= 4.0 – 3.5 = 0.5A
(iii) 1/RC = (frac{1}{R}) + (frac{1}{R_2})
1/1.75 = (frac{1}{R}) + (frac{1}{2})(frac{1}{R}) = 1/1.75 – (frac{1}{2})
R = 14Ω