A solid plastic sphere of radius 10.0 cm has charge with...

Name: A solid plastic sphere of radius 10.0 cm has charge with uniform density throughout its volume. The electric field 5.00 cm from the center is 86.0 kN/C radially inward. Find the magnitude of the electric field 15.0 cm from the center.
Uploaded: 2021-09-11T19:21:48-08:00
Duration: 7 min 51 s
Channel: Umar Sohail Qureshi
Description: A solid plastic sphere of radius 10.0 cm has charge with uniform density throughout its volume. The electric field 5.00 cm from the center is 86.0 kN/C radially inward. Find the magnitude of the electric field 15.0 cm from the center.

A solid plastic sphere of radius 10.0 cm has charge with uniform density throughout its volume. The electric field 5.00 cm from the center is 86.0 kN/C radially inward. Find the magnitude of the electric field 15.0 cm from the center.

Transcript

00:01 High in the given problem there is a plastic solid charged sphere having a radius of 10 centimeter then there is a point within this plastic sphere at a distance of r1 and electric field at this point is given as 86 kilo newton per gullum the distance is r1 is equal to 5 .0 centimeter and electric field at this point has been given as we may assume it to be even, which is having a value of it is 6 .0 kilo -neuton per coulomb.

00:53 If we consider a gaussian surface passing through this point, observation point, the gaussian surface is in the form of a navigation point.

01:06 Concentric sphere so applying goss's law at this point electric field e1 multiplied by the surface area of this gaussian surface which is 4 pi r1 square should be equal to the charge and closed within this gaussian surface divided by epsilon not so if we consider volume charge density to be row of this plastic sphere if volume charge density is considered to be row then this charge within this volume comes out to be 4 by 3 pi r1 cube multiplied by row so we can say here it becomes even into 4 pi r1 square is equal to 4 by 3 pi r1 cube into row divided by epsilon not solving all these values means canceling the similar terms on both the sides we get an expression for electric field as e1 is equal to r1 times row divided by 3 epsilon not as we cancel this 4 pi from both the sides and this r1 square with the cube of r1 now using the given data we can find the value of this volume charge density here it comes out to be three times of even multiplied by epsilon not divided by r1 so it becomes the volume charge density so plugging in all the known values it becomes three times of 8 .854 into 10 dash minus 12 coularn square per newton meter square multiplied by electric field which was minus 86 into 10 dash par 3 newton per coulin and this negative sign has been used because the electric field is directed into this is a plastic sphere is here radially inward so now when we calculate all these values and it is having in the denominator the radius of the sphere also which was 0 .05 meter so solving all these values we get the volume charge density as minus 4 .4 5 .7 into 10 dash to bar minus 5 column per meter cube...

Question

A solid plastic sphere of radius 10.0 cm has charge with uniform density throughout its volume. The electric field 5.00 cm from the center is 86.0 kN/C radially inward. Find the magnitude of the electric field 15.0 cm from the center.

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