Question

6 of 39 Questions Assignment Score: 439/3900 Resources Hint Check Answer Press |Esc to exit full screen 2 of o AttemptsComect Question 6 of 39> 3 Question 100% A honey bee of mass 130 mg has accumulated a static charge of +1.4 pC. The bee is returning to her hive by following the path shown in the figure. Because Earth has a naturally occurring electric field near ground level of around 100 V/m pointing vertically downward, the bee experiences an electric force she ies 1 of oo Attempts corect 4 Question 10096 1ofoo Artema ts Correct 5 Question 2 of o Attempts In Frogress 4B/100 What is the change in the bee's electric potential energy ΔΙ.lectric, as she flies from point A (0 m, ().3 m) to point B (5.1 m, 3.7 m)? 0/100 7 Question 0/100 Δυ,lectric- 0/100 Compute the ratio of the bee's change in electric potential energy to her change in gravitational potential energy 9 Question 0 of Attemots 0/100 10 Question 0/100 0 of oo Attempts 11 Question 0/100

Answer 1

Given:

Mass of honey bee = 1.30 mg = 1.30* 10^-6 kg

Charge q on honey bee = 1.4 pC= 1.4* 10^-12 C

( Earth) Electric field = 100 V/m (downward)

Initial coordinate of bee is A (0, 0.3m)

Final coordinate of bee is B ( 5.1m ,3.7m)

Part (1)

Change in Electric potential energy:

Since Electric field is constant near surface and acts in downward direction.

So change in potential difference (∆v) due to change in position of bee from A to B = (- E * displacement along y direction)

Note : change in displacement along X axis has no role in changing potential difference as electric field is directed downward in direction and hence , ∆ v along x  

direction = 0 , ( ∆ v = E * ds *cos90°= 0)

Now ∆V = E * (Y_{​​​​​B} - Y_{​​​​​​A})

∆V = - 100 * (3.7- 0.3) V

∆V = -340V

So , change in electrostatic potential energy, ∆ U is given by

∆ Uelec = q∆ V

∆Uelec= -1.4*10^(-12) * 340

∆ Uelec = -4.76 * 10^ (-10) J

Part (2)

Gravitational potential energy =- (m *g * h)

Change in gravitational potential energy ,( ∆Ug)

= -m* g* (Y_{​​​​​​B -} Y_{​​​​​​A)}

= -1.30 * 10 ^ (-6) * 9.8 * (3.7- 0.3)

= -4.33602* 10^( -5)

Now ∆ U _electric / ∆ U grav

= {-4.76* 10^(-10)}/{- 4.33602*10^(-5)}

= 1.0977* 10* ^( -5)

Note : Gravitational potential energy and electrostatic potential energy are path independent , hence consider bee's initial and final position coordinate only . As both force is conservative in nature.