Question

1) a car battery is rated at 90 amphour. How much charge is available in the battery?

2) A +2.6 uc point charge is placed at the center of a cube with sides of length 7.5cm. What is the electric flux through two sides of the cube?

3) The amount of charge flowing though a circuit caries with time according to.. q(t)=(0.2t²-0.3t), with q in coulombs and t in seconds. Find the current through the circuit at t = 1.5 seconds.

4) Calculate the acceleration of an electron placed in a uniform electric field of magnitude 4.5*10⁵ N/C.

Answer 1

1)

i = current = 90 A

t = time of operation = 1 hour = 60 min = 60 x 60 sec = 3600 sec

charge available on the battery is given as

Q = i t

Q = (90) (3600)

Q = 3.24 x 10⁵ C

2)

n = number of faces of cube = 6

Q = total charge enclosed by the cube = 2.6 x 10^-6 C

Total electric flux through each side of the cube is given as

= Q/(n) = 2.6 x 10^-6 /(6(8.85 x 10^-12)) = 4.9 x 10⁴ Wb

electric flux through two sides is given as

' = 2 = 2 (4.9 x 10⁴) = 9.8 x 10⁴ Wb

3)

Current is given as

i = dq/dt

i = (d/dt) ((0.2) t² - (0.3)t)

i = (0.4) t - 0.3

i = (0.4) (1.5) - 0.3

i = 0.3 a

4)

E = magnitude of the magnetic field = 4.5 x 10⁵ N/C

q = magnitude of charge on electron = 1.6 x 10^-19 C

m = mass of the electron = 9.1 x 10^-31 kg

acceleration of electron due to electric field is given as

a = qE/m

a = (1.6 x 10^-19) (4.5 x 10⁵)/(9.1 x 10^-31)

a = 7.91 x 10¹⁶ m/s²