Assignment 2
1. Given Electric field E= (3𝑥 2 + 𝑦)𝑥̂+x𝑦̂kV/m.
Find the work done (in mJ) moving a -2µC
charge from (0, 5, 0) to (2,-1, 0) by taking the
path
(0, 5, 0) (2, 5, 0) (2,-1, 0)
2. In above problem if path is along the line y=5-3x
Then work done is
(a) 12 mJ (b) 10 mJ (c) 16 mJ (d) 20mJ
3. An electric field is expressed in Cartesian
coordinate system by E= 6𝑥 2 𝑎𝑥 +6y𝑎𝑦 +4𝑎𝑧 .If
points M and N specified by M(2,6,-1) and N(-3,-
3,2).Then 𝑉𝑀𝑁 is
a. -143 V (b) -123 V (c) -139 V (d) 0 V
4. If the potential as a function of position is given
by V=2𝑥 2 +3y+6𝑧1/2 V. The magnitude of electric
field at the point x=y=z=0.5 m is
(a) 3.58 V/m (b). 4.58 V/m (c) 0 V/m (d) none
5. Let the V is absolute potential at a point P which
is 2 m from a point charge Q=+5µC and let W is
work required to move a +8nC charge from
infinity to P. then the V and W are
(a) 22.5 kV and 180 µJ
(b) 2.5 kV and 80 µJ
(c) 122.5 kV and 180 µJ
(d) 0 kV and 0 µJ
6. Two point charges -4 µC and +5 µC are located at (2,-1,
3) and (0,4,-2) respectively. Find the potential at (1, 0, 1).
(Assuming zero potential at infinity).
(a) -5.87 kV
(b) -55.87 kV
(c) -15.87 kV
(d) -2.87 kV
7.A point charge of 5nC is located at origin. If V=2V
at (0,6,-8) then potential at (-3,2,6) is
(a) 2.1 V
(b) 0.87 V
(c) 1.93 V
(d) 3.93 V
8. If we are saying that Electrostatic field is
conservative, we do not mean that
(a) It is gradient of scalar field.
(b) Its curl is identically zero.
(c) The work done in a closed path inside the field is zero
(d) The potential difference between any two point is
zero.
9. A uniform surface charge density of 20nC/𝑚2 is
present on the spherical surface r=0.6 cm in free space.
The absolute potential at P( 1cm, 250 , 500 ) is
(a) 6 V
(b) 7.2 V
(c) 8.14 V
(d) 0 V
10. In the above what is 𝑉𝐴𝐵 if A( 2cm, 300 , 600 ) and
B( 3cm, 450 , 900 ).
(a) 1.36 V
(b) 0.36 V
(c) 5.36 V
(d) 8.14 V
11.Given the potential field V= 2𝑥 2 𝑦 - 5z and a point
P(-4,3,6) the volume charge density at point P is
(a) -91 pC/𝑚3
(b) -106.2 pC/𝑚3
(c) -11 pC/𝑚3
(d) -21 pC/𝑚3
(12) A sphere of radius 𝑟1 = 30 cm has a charge
density variation with radius given by 𝜌0 𝑟/𝑟1 .where
𝜌0 =200 pC 𝑚−3 .The total charge of the sphere (in
pC)
(13) In the region of free space where 2<r<3,
𝑘
0.4𝜋<θ<0.6𝜋 and 0<φ< 𝜋/2 ,let E= 2 𝑎𝑟 . The
𝑟
positive value for k so that energy stored is exactly
1 J.
(a) 1.18 * 106 V m.
(b) 5.18 * 106 V m.
(c) 4.18 * 106 V m.
(d) 2.18 * 106 V m.
5𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜙
14.Given the field D= 𝑎𝑟 C/𝑚2 . Then the
𝑟
total charge contained in the region r<2m is
15. In the above question the total flux leaving the
surface r=2m is
16. Let D= 5 𝑟 2 𝑎𝑟 mC/𝑚2 for r< 0.08m and D=
0.1𝑎𝑟 /𝑟 2 C/𝑚2 for r>0.08m. The 𝜌𝑣 for r=0.06m is
(a) 4 mC/𝑚3
(b) 1.2 mC/𝑚3
(c) 0 mC/𝑚3
(d) none
17. In the above question The 𝜌𝑣 for r=0.1m is
(a) 4 mC/𝑚3
(b) 1.2 mC/𝑚3
(c) 0 mC/𝑚3
(d) none
18. The electric flux density is given as D= 20𝜌3 𝑎𝜌
2 𝑎𝜌
C/𝑚 for 𝜌<100µm and k for 𝜌>100µm. The
𝜌
value of k so that D is continuous at 𝜌=100µm.
(a) 1* 10−15 C/m
(b) 7* 10−15 C/m
(c) 2* 10−15 C/m
(d) discontinuous everywhere
(19) If D= 2r 𝑎𝑟 C/𝑚2 . The electric flux leaving the
surface of the cube 0<x,y,z<0.4 is
(a) 0.29 C
(b) 0.38 C
(c) 1.2 C
(d) 5.2 C
(20) A potential field in free space is expressed as
20/xyz V. The total energy stored within the cube
1<x,y,z<2 is (in pJ)
(21) Four 0.8 nC point charges are located in free
space at the corners of a square 4cm on a side. The
total potential energy stored is
(a) 1.2 µJ (b) 2.2 µJ (c) 0.78 µJ (d) 0.61 µJ
22. The D at (4,0,3) if there is a point charge -5πµC
at (4,0,0) and a line charge 3π mC/m along the y-
axis is
(a) 240𝑥̂ + 42𝑧̂
(b) 1.23𝑥̂ − 4.1𝑦̂ + 𝑧̂
(c) 240𝑥̂ + 4.1𝑦̂ + 42𝑧̂
(d) none
23. Consider a spherical shell with radius a with
charge density 𝜌𝑠 C/ 𝑚2 The value of E-field
between the 0<r<a is zero . Then the potential in
this region must be
(a) zero (b) constant (c) infinite (d) none
24. The divergence of vector 𝐴̅=y𝑧𝑥̂ + 4𝑥𝑦𝑦̂ + y 𝑧̂
at(1, -2,3) is
25. The divergence of vector
ρzsinφ𝑎𝜌 +3ρ𝑧 2 𝑐𝑜𝑠𝜙𝑎𝜙 at (5,π/2,1) is
26.Vector 𝐴̅= 3𝑦̂ + 2 𝑧̂ and Vector𝐵̅=5𝑥̂ + 8𝑦̂ extend from
the origin. The dot product between 𝐴̅ & 𝐵̅ and angle
between them are:
(a) 24 , −45.110 (b) 24, 45.110
(b) 12, 300 (d) 12, −45.110
27.Given that Vector 𝐴̅=𝑥̂ + 5𝑦̂ + 3 𝑧̂ and vector 𝐵̅=-2𝑥̂ -
5𝑦̂ + k𝑧̂ are perpendicular then the value of k is
28.The cross product between vector 𝐴̅=8𝑥̂ + 3𝑦̂ - 10𝑧̂ and
Vector 𝐵̅=-15𝑥̂ + 6𝑦̂ + 17𝑧̂ is
(a) 111𝑥̂ + 14𝑦̂ + 93𝑧̂
(b) 111𝑥̂ - 14𝑦̂ + 93 𝑧̂
(c) -111𝑥̂ + 14𝑦̂ -93 𝑧̂
