Question

An electric dipole is formed from two charges, , spaced 1.0 cm apart. The dipole is at the origin, oriented along the y-axis. The electric field strength at the point (x,y) = (0,10) in cm is 360 N/C. a. Calculate the dipole moment and charge q. b. Calculate the electric field strength at the point (x,y) = (10, 0) in cm.

Answer 1

a. dipole moment = 2.003 × 10⁻¹³ Cm, charge = 2.003 × 10⁻¹¹ C b. 8.96 N/C

Step-by-step explanation:

a. The electric field due to a dipole is given by

E = p/2πεy³ where p = dipole moment and y = distance of dipole to point of electric field = 10 cm = 0.10 m. E = electric field strength at (0,10) = 360 N/C

So, E = p/2πεy³

p = 2πεy³E = 2π × 8.854 × 10⁻¹² × (0.10 m)³ × 360 N/C = 2.003 × 10⁻¹³ Cm

Also, p = qd where q = charge and d = distance of charges apart = 1.0 cm = 0.01 m

q = p/d = 2.003 × 10⁻¹³ Cm/0.01 m = 2.003 × 10⁻¹¹ C

b. The electric field at point (10,0)

E = qx/[πε√(d² + 4x²)]³ which is the electric field at an axis perpendicular to the dipole where x = 10 cm = 0.10 m

E = 2.003 × 10⁻¹¹ C × 0.10/π × 8.854 × 10⁻¹²√(0.01² + 4×(0.1)²)³ = 8.96 N/C.

Answer 2

q = 3.703*10^-9

dipole moment = 3.703*10^-11

E @ (10,0) = 331.977 N/C

Step-by-step explanation:

Given:

Coordinates

+ q = (0,-0.5) cm

- q = (0,0.5) cm

E = 360 N/C @ (0,10)

Solution:

`Electric Field Strength @ (0,10) = (k*q)/(R^2)\\`

Note: +q (away from charge) and -q (towards the charge)

`E = k*q*((1)/(R^2_(1)) - (1)/(R^2_(2) ))\\ 360 = (9*10^9)*q*((1)/(0.095^2) - (1)/(0.105^2 ))\\\\q =1.99 *10^-9`

Dipole moment = q.(space between two charges)

= (3.703*10^-9 * 0.01)

= 3.703*10^-11

Electric Field Strength @ (10,0)

`E = 2*k*q*((1)/(R^2))*cos(Q)\\ \\Q = arctan((10)/(0.5)) = 87.138 degrees\\R = √(10^2 + 0.5^2) = 10.01249 cm\\E = 2* (9*10^9)*(3.703*10^-9)*(cos (87.138))/(0.1001249^2)\\E = 331.977 N/C`