A point charge of -3.00 μC is located in the center of a spherical cavity of radius 6.60 cm inside an insulating spherical charged solid. The charge density in the solid is 7.35 × 10 −4 C/ m^3 .Part A Calculate the magnitude of the electric field inside the solid at a distance of 9.40 cm from the center of the cavity. Express your answer with the appropriate units. Part B Find the direction of this electric field.

Question
Asked Sep 7, 2019
1 views

A point charge of -3.00 μC is located in the center of a spherical cavity of radius 6.60 cm inside an insulating spherical charged solid. The charge density in the solid is 7.35 × 10 −4 C/ m^3 .

Part A Calculate the magnitude of the electric field inside the solid at a distance of 9.40 cm from the center of the cavity. Express your answer with the appropriate units.

Part B Find the direction of this electric field.

check_circle

Expert Answer

Step 1

Given:

Charge at the centre of the spherical cavity, Q = -3.00 µC

Radius of the spherical cavity, Ri = 6.60 cm = 6.60 ×10-2 m

Volume charge density of the spherical charged solid = 7.35×10-4 C/m3

Step 2

Consider a Gaussian sphere of radius R0 = 9.40cm = 9.40 ×10-2 m from the centre of the spherical cavity.

Write the expression for charge enclosed by the Gaussian sphere:

4
=-I
genclosed
3
(Ri-Ri)p+Q..(1)
(Where p is the volume charge density, Ri is the radius of the cavity, Ro is the radius
of the gaussian surface, and Q is the charge at the center of the cavity)
Substitute 9.40 cm for Ro, 6.60 cm for Ri, -3.00HC for Q and 7.35x10-4C/m3 for
p in the equation (1)
4
((9.40x10 m)-(6.60x10 m(7.35x10 C/m2)+(-3x 1oC)
enc
3
enciosed (1.671x10 C)-(3x10C)
Leneiaced =-1.33x10-C
help_outline

Image Transcriptionclose

4 =-I genclosed 3 (Ri-Ri)p+Q..(1) (Where p is the volume charge density, Ri is the radius of the cavity, Ro is the radius of the gaussian surface, and Q is the charge at the center of the cavity) Substitute 9.40 cm for Ro, 6.60 cm for Ri, -3.00HC for Q and 7.35x10-4C/m3 for p in the equation (1) 4 ((9.40x10 m)-(6.60x10 m(7.35x10 C/m2)+(-3x 1oC) enc 3 enciosed (1.671x10 C)-(3x10C) Leneiaced =-1.33x10-C

fullscreen
Step 3

(A) Calculate the electric field at the distance ...

Using Gauss's law we can wrtie the electric field at the distance Ro = 9.40cm,
E(4TR2)
enc
1 qenc
Rearranging for Electric field, E
Απε, R
1
9x10° Nm2/C?, qored=-1.33 x10 C and Ro = 9.40x 10-2m:
4πε.
Substitute
E (9x10 Nm2 /c(-1.33x10°C)
(9.40 x10 m)
E -1.35x 106N/C
Hence, Magnitude of electric field is 1.35x10'N/C
help_outline

Image Transcriptionclose

Using Gauss's law we can wrtie the electric field at the distance Ro = 9.40cm, E(4TR2) enc 1 qenc Rearranging for Electric field, E Απε, R 1 9x10° Nm2/C?, qored=-1.33 x10 C and Ro = 9.40x 10-2m: 4πε. Substitute E (9x10 Nm2 /c(-1.33x10°C) (9.40 x10 m) E -1.35x 106N/C Hence, Magnitude of electric field is 1.35x10'N/C

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Science

Physics

Electric Charges and Fields

Related Physics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: A 600.00 N ballast is hung from the end of a wire of cross-sectional area 0.0000010 m^2. The wire st...

A: a)The stress on the wire is,

question_answer

Q: What is 28 mg coverted into kilograms? I put 2.8 e-5 and it was incorrect on Webassign.

A: 28 mg can be converted as follows.

question_answer

Q: When a shower is turned on in a closed bathroom, the splashing of the water on the bare tub can fill...

A: (a)Write the expression for the electric flux .

question_answer

Q: An object that weighs 75 N is pulled on a horizontal surface by a horizontal pull of 50 N to the rig...

A: Given weight of the object =75 NWeight = mg =75Mass of the object = 75/g = 75/9.8  = 7.653 kg.Pullin...

question_answer

Q: A thin rod consists of two parts joined together. Two-fifths of it is silver and three-fifths is gol...

A: The fractional decrease in length of the rod=∆LThe initial length of the silver rod=L0,silverThe ini...

question_answer

Q: In the Olympic shotput event, an athlete throws the shot with an initial speed of 13.0 m/s at a 42.0...

A: Time taken to reach maximum height is,

question_answer

Q: An electric field given by = 4.8 - 2.7(y2 + 7.5) pierces the Gaussian cube of edge length 0.460 m an...

A: The figure with the direction vectors is shown below:

question_answer

Q: the sound in the united center during a Chicago Bulls basketball game in 1998 was seven times as int...

A: The decibel rating today = 89dB.The intensity of sound in 1998 is 7 times as that of today.

question_answer

Q: Can you show me how to work this? I’m thinking I’m getting confused on the units. Thanks!

A: The ideal gas equation is,