A point charge of -2.01 mu C is located in the center of a spherical cavity of r
ID: 1607622 • Letter: A
Question
A point charge of -2.01 mu C is located in the center of a spherical cavity of radius 6.53 cm inside an insulating spherical charged solid. The charge density in the solid is 7.34 times 10^-4 C/m^3. Calculate the magnitude of the electric field inside the solid at a distance of 9.49 cm from the center of the cavity. Express your answer using two significant figures. Find the direction of the electric field inside the solid at a distance of 9.49 cm from the center of the cavity. The electric field points radially outward. The electric field points radially inward. The electric field is zero.Explanation / Answer
A point charge = q = -2.01*10^-6 C is located in the center of a spherical cavity of radius = r =6.53*10^-2 m inside an insulating spherical charged solid.
The charge density in the solid = d = 7.34×104 C/m^3.
Distance from the center of the cavity.= R =9.4*10^-2 m
Volume of shell of charge= V =(4pi/3)[ R^3 - r^3 ]
Charge on the shell = Q =V*charge density'd'
Q =(4pi/3)[ R^3 - r^3 ]*d
Q = 4.1888*10^-4 [8.57375 - 2.81011 ]*7.34*10^-4
Q = 4.1888*10^-4 [5.76364 ]*7.35*10^-4
Q =2.4143*10^-4 *7.35*10^ -4
Q =1.7745*10-6 C
Electric field at 9.49*10^-2m due to shell = E1 =kQ/R^2
E1 =9*10^9*1.7745*10^-6 / 90.25*10^-4
E1 =1.769*10^6 N/C
Electric field at 9.49*10^-2m due to 'q' at center = E2 =kq/R^2
E2 = - 9*10^9*2.14*10^-6 / 90.25*10^-4
E2 =2.134*10^6 N/C
The magnitude of the electric field inside the solid at a distance of 9.49cm from the center of the cavity = E2- E1=[ 2.134 - 1.769 ]*10^6 = 3.65*10^5 N/C
a)
The magnitude of the electric field inside the solid at a distance of 9.49cm from the center of the cavity 3.65*10^5N/C
b )
The electric field points radially inward.
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