1. If the z-axis carries a linear charge density of 8 nC/m, what is the magnitud

Question

1. If the z-axis carries a linear charge density of 8 nC/m, what is the magnitude of the electric field at the point (6 cm, 2 cm, 0 cm)?

2. Two concentric shells with radii r1= 7 cm and r2= 16 cm carry changes q1 = 15 nC and q2 = 12 nC respectively. Find the electric field at a distance of 10 cm from the center.

3. Three thin wires carrying equal linear charge densities of 3 nC/m are locatedd along the x, y and z axes respectively. What is the electric flux through a spherical surface of radius 10 cm centered at the origin?

4. There is a uniform electric field of 453 V/m in the +y direction everywhere in the xy-plane. What is the potential diffference Vb-Va between point b with coordinates (2 cm, 7 cm) and point a with coordinates (5 cm, -4cm)?

Explanation / Answer

Q1.

1. as we know, electric field due to an infinite linear charge density is radial in nature and given by

E=q_l/(2*pi*epsilon*r)

where r=radial distance

q_l=linear charge density

epsilon=electrical permitivity of the medium=8.85*10^(-12) for vacuum

so at (6 cm,2 cm, 0 cm), r=sqrt(6^2+2^2) cm=6.3245 cm

then using the values,

electric field=8*10^(-9)/(2*pi*8.85*10^(-12)*6.3245*10^(-2))

=2274.78 N/C=2.27 kN/C

hence option e is correct.

Q2.using gauss law:

epsilon*electric field*4*pi*r^2=total charge enclosed

where r =radius of gaussian sphere

here r=0.1 m

charge enclosed=q1=15 nC

then electric field=15*10^(-9)/(4*pi*8.85*10^(-12)*0.1^2)=13487 N/C=13.5 kN/C

hence option b is correct.

Q3. electric flux=total charge enclosed (gauss' law)

==>electric flux through the sphere centered at origin=charge enclosed in 20 cm of x axis+charge enclosed in 20 cm of y axis+charge enclosed in 20 cm of z axis

(20 cm is diameter of the sphere and the length of the segment of the three axes enclosed by the sphere)

=3*0.2+3*0.2+3*0.2 nC

=1.8 nC

hence flux through the spherical surface is 4.5 nC

Q4. potential difference from a to b=integration of -E.dl

here dl=dy

(as E field exists only along y direction)

hence potential difference=-453*(7-(-4))*0.01

=-49.83 volts

hence option d is correct.

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