Question

Four identical charged particles of charge 1 μC, 2 μC, 3 μC and 4 μC are placed at x = 1 m, x = 2 m, x = 3 m and x = 5 m. The electric field intensity at origin is a. 17.94 kN/C b. 24.3 kN/C c. 20.68 kN/C d. 18.88 N/C

Answer 1

Given :

The distance of 1 μC from origin = 1 m

The distance of 2 μC from origin = 2 m

The distance of 3 μC from origin = 3 m

The distance of 4 μC from origin = 5 m

To find :

The electric field intensity at the origin due to the charges .

Solution :

Electric field intensity = ( k * q ) / ( r * r )

where , r is distance ,

k = 9 * 10^9 ,

and , q is charge .

now ,

electric field intensity at the origin = [ k * 10^(-6) / 1 * 1 ] +[ k * 2 * 10^(-6) / 2 * 2 ] + [ k * 3 * 10^(-6) / 3 * 3 ] + [ k * 4 * 10^(-6) / 5 * 5 ]

=> electric field intensity at the origin = k * 10^(-6) [ 1 + 1/2 + 1/3 + 4/25 ] N/C

=> electric field intensity at the origin = 9 * 10^9 * 10^(-6) * 1.99 N/C

=> electric field intensity at the origin = 17.94 kN/C

The electric field intensity at the origin due to the charges is 17.94 kN/C .