Question

The following scenarios will ask you to compare the electric field at point P for four differnet situations. Situation B: Situation D: 20) ·P 1/2R Situation A: Situation C: 2Q 1/2R How does the magnitude of the electric field at P compare for Situations A and B? EA EB EA-2EB AEB O EA EB EA-4EB How does the magnitude of the electric field at P compare for Situations A and C? EA=Ec EA 2E EA E 4 TC How does the magnitude of the electric field at P compare for Situations A and D? EA-8ED EA-4ED EA2ED

Answer 1

Electric field due to a point charge at distance 'r' is given by:

E = k*q/r^2

where direction of electric field is towards the negative charge and away from positive charge.

Part A.

Electric field at P for situations A and B

At point A:

E_A = k*Q_A/r_A²

Given that, Q_A = Q, and r_A = R, So

E_A = k*Q/R²

At point B:

E_B = k*Q_B/r_B²

Given that, Q_B = Q, and r_B = R/2, So

E_B = k*Q/(R/2)² = 4*k*Q/R²

E_B = 4*E_A

E_A = (1/4)*E_B

Correct option is A.  

Part B.

Electric field at P for situations A and C

At point A:

E_A = k*Q_A/r_A²

Given that, Q_A = Q, and r_A = R, So

E_A = k*Q/R²

At point C:

E_C = k*Q_C/r_C²

Given that, Q_C = 2Q, and r_C = R, So

E_C = k*2Q/(R)² = 2*k*Q/R²

E_C = 2*E_A

E_A = (1/2)*E_C

Correct option is D.  

Part C.

Electric field at P for situations A and D

At point A:

E_A = k*Q_A/r_A²

Given that, Q_A = Q, and r_A = R, So

E_A = k*Q/R²

At point D:

E_D = k*Q_D/r_D²

Given that, Q_D = 2Q, and r_D = R/2, So

E_D = k*2Q/(R/2)² = 8*k*Q/R²

E_D = 8*E_A

E_A = (1/8)*E_D

Correct option is D.