Question

A spherical balloon has a radius o R-70 cm, and its surface has been charged uniform a) Calculate the field strength ri 54 cm from the balloon's centre b) Calculate the field strength r2-191 cm from the balloon's centre (c)Calculate the net charge on the balloon. You measure the elec c field to be = at he balloons sur ace where N PAPER SOLUTION Solve the problem on paper first, including all four IDEA steps. You will become a better physicist that way! Have you finished your paper solution already? ⓔyes INTERPRET DEVELOP In your answers below type r1. r2, and Es to represent r1. 2. and E. If needed, please use k rather than Eo Derive an algebraic expression for the electric field at r1 E1- Derive an algebraic expression for the electric field at T2 Derive an algebraic expression for the net charge on the balloon. EVALUATE

Answer 1

a)

R = radius of the balloon

70 cm = 0.70 m

let the gaussian surface of radius , r₁ = 54 cm = 0.54 m

Q_enclosed = change enclosed by the gaussian surface = 0 (since all the charge is at surface of balloon at distance 70 cm )

Using gauss's law

E A = Q_enclosed / $\epsilon$

E A = 0

E = 0

b)

Electric field at any distance greater than or equal to radius of balloon is given as

E = k Q/r²

so E $\alpha$ 1/r²

hence E_surface /E₂ = r₂²/r₁²

25000/E₂ = (191)² /(70)²

E₂ = 3.4 x 10³ N/c

c)

at the surface electric field is given as

E_s = k Q/R²

25000 = (9 x 10⁹) Q/(0.70)²

Q = 1.4 x 10^-6 C