Reference no: EM132433600

Assignment - Electromagnetic Theory

Q1. Consider the vectors A^- = 2x^{^} + y^{^} - 2z^{^}, B^- = 3x^{^} - 4y^{^} and C^- = x^{^} + y^{^} + 2z^{^}. Then the values of K for which |KB| = 2 is.

(a) ±0.2 (b) ±0.3 (c) ±0.4 (d) ±1

Q2. In the previous question the value of 2A^- - 3B^-/|C| is

(a) -5x^{^} + 14y^{^} - 4z^{^}/√6

(b) x^{^} + y^{^} + z^{^}

(c) x^{^} + y^{^} + z^{^}/√3

(d) None of these

Q3. Consider the vectors F^- = 2x^{^} - 6y^{^} + 10z^{^}, G^- = x^{^} + G_yy^{^} + 5z^{^}. If F and G have the same unit vector.

Then the value of G_y is

(a) 6 (b) 0 (c) -3 (d) 2

Q4. Consider the vectors A^- = 10x^{^} - 4y^{^} + 6z^{^}, B^- = 2x^{^} + y^{^} and C- = -x^{^} + z^{^}. Then the unit vector in along A^- + 2B^- - C^- is

(a) 0.94x^{^} - 0.125y^{^} - 0.32z^{^}

(b) 0.94x^{^} + 0.125y^{^} + 0.32z^{^}

(c) 0.94x^{^} - 0.125y^{^} + 0.32z^{^}

(d) x^{^} + y^{^} + z^{^}

Q5. Points P and Q are located at (2, 0, 4) and (1, 5, 3) let a vector X which is parallel to PQ and having magnitude 5. Then the vector X is

(a) -0.96x^{^} + 4.81y^{^} - 0.96z^{^}

(b) 1.23x^{^} - 4.1y^{^} + z^{^}

(c) 0.96x^{^} - 4.81y^{^} + 1.23z^{^}

(d) None of these

Q6. The component of vector 3x^{^} + y^{^} - 2z^{^} along 4x^{^} + 3y^{^} is.

(a) 6 (b) 3 (c) -3 (d) 1.23x^{^}

Q7. In Cartesian coordinate system, the range of x, y, z

(a) - ∞ < x < ∞, - ∞ < y < 0, 0 < z < ∞

(b) - ∞ < x < ∞, - ∞ < y < ∞,- ∞ < z < ∞

(c) 0 < x < ∞, 0 < y < ∞, 0 < z < ∞

(d) - ∞ < x < 0 , - ∞ < y < 0, - ∞ < z < 0

Q8. Consider the Point P (-2, 6, 3) and vector A^- = yx^{^} + (x + z)y^{^} + z z^{^} .The vector A at point P in the rectangular co-ordinate system and unit vector along it respectively are

(a) x^{^}+3y^{^}+5z^{^}, (x^{^}+3y^{^}+5z^{^})/√35

(b) 6x^{^}+y^{^}+3z^{^}, (6x^{^}+y^{^}+3z^{^})/√46

(c) x^{^}+y^{^}+z^{^}, (x^{^}+y^{^}+z^{^})/√3

(d) x^{^}+2y^{^}, (x^{^}+2y^{^})/√5

Q9. The Point charges 3mc & -2mc & -4mc are located at (1, 1,-1) & (-1, 1, 4) and (3, 2,-1) respectively. The electric force on a 10nc charge located at (0, 2, 1) is

(a) 1.8x^{^} + 5.85y^{^} + 13.5z^{^} mN

(b) 13.5x^{^} + z^{^} mN

(c) 5.85y^{^} + 1.8x^{^} mN

(d) 1.8x^{^} - 5.85y^{^} mN

Q10. Point charges Q₁ = 1nc and Q₂ = -1nc are at a distance apart. Which of the following statement is incorrect?

(a) The force on Q₁ is attractive.

(b) The force on Q₂ is along the line joining them.

(c) A point charge Q₃ = -3nc located at the midpoint between along Q₁ and Q₂ experiences no net force.

(d) As the distance between them decreases, the force on Q₁ increases linearly.

Q11. Two charges +Q and +2Q are separated by a distance 1m. A third charge is located such that the electrostatic system is in equilibrium. The location (take from +Q) and the value of third charge in terms of Q respectively are

(a) 0.5m, Q/2

(b) 0.5m, Q/4

(c) 0.25m, -Q/2

(d) 0.5m, -Q/4

Q12. Consider a Two point charges of values +Q are located at a distance d apart. The Force between them are F.

If charge values doubled and distance between them is halved by original values. Then new force F₁ Becomes

(a) 4F (b) 8F (c) 16F (d) 64F

Q13. Consider Four identical point charges of values +15µc are located at the corners of a square defined by -1<x, y<1, z=0. The force on the 10µc point charge by which is located at the centre of the square is

(a) 1.072z^{^} (b) 1.072y^{^} (c) 1 N (d) 0 N

Q14. Two spheres having charges 20µc and -5µc are allowed to touch each other and then placed 25.0cm apart.

Then

(1) What charge is transferred between the spheres?

(2) What force exist when they apart by 25 cm.

Q15. At what distance of separation must two 1µc charges be positioned in order for the repulsive force between them to be equivalent to the weight (on earth) of a 1kg mass?

(a) 0.1 m (b) 0.2m (c) 0.02m (d) 0.03m