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# One Shot Marathon Series Test - EMFT (ECE+EE)

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Question 1

Given solenoid vector , then the value of b is

Question 2

If the electric field V/m and, then the displacement current passing through an area of at is

Question 3

A sphere of radius R centred at origin contains a uniformly distributed charge within it with a charge density is e0 C/m3. The ratio of the magnitude of electric field intensity is R/3 and 3R from its centre ____

Question 4

Three identical point charges of 4 pC each are located at the corners of an equilateral triangle 0.5 mm on a side in free space. How much work must be done to move one charge to a point equidistant from the other two and on the line joining them?

Question 5

Given the current density , the total current crossing the plane y = 1 in the direction in the region 0 < x < 1, 0 < z < 2 is

Question 6

A sphere radius r1 = 30 cm has a charge density variation with radius given by , where ρ0 = 200 pC/m3. The total charge of the sphere (in pC) is?

Question 7

The variation of potential with distance r from a fixed point is as shown below. The electric field at r = 5 m is______ V/m

Question 8

Two point charges of 6 nC are located at (1, 0, 0) and (-1, 0, 0) in free space. If there exist maximum value of potential at any point, which is lying on z-axis, then the maximum potential (in volts) is_____.

Question 9

Calculate volume charge density( in C/m3) at (2, -4, 6) if the electric flux density is given as:

C/m2

Question 10Multiple Correct Options

The surfaces ρ = 3 and 5, ϕ = 100° and 130° and z = 3 and 4.5. Find the volume enclosed, total area of the enclosing surface and total length of the twelve edges of the surface.

Question 11

Consider a scalar magnetic potential, Vm = 2x2 + 4x – 2y2 A in a certain region of free space. Then the vector force exerted on a straight wire segment in the region if it extends from origin to a point (1, 0, 0) and carries 5 A in the direction?

Question 12

Match the lists I with the list II

List 1 - List 2

(A) Gauss law - 1)

(B) Continuity equation - 2)

(D) Ampere’s law - 4)

Question 13

A linear, homogeneous, isotropic dielectric material has ϵr = 3.6 and is covering the space between z=0 to z=1. If V = -6000z V in the material, find E and polarization P.

Question 14

A uniform surface charge density of 20 nC/m2 is present on the spherical sphere r = 0.6 cm in free space. Find the absolute potential at P(r = 1 cm, θ = 25°, ϕ = 50°) in (volts)

Question 15

Two uniform vector fields are given by E = –7aρ + 5aϕ + 3az and F = aρ + 3aϕ – 9az.

The vector component of E at P(7, π/2, 3) parallel to line.

x = 2, z = 3 will be?

Question 16

The finite sheet 0on the z=0 plane has a charge density nC/. The total charge on the sheet is …….nC

Question 17

On X- axis, some charge is placed. The electric potential at a point is V = 4x2 + 10x –6 What is the electric field ( in V/m) at x = 0.8

Question 18

If V = x2y (z+3) v then calculate the magnitude of charge within the cube 0 < x, y, z < 1 _______ (in pC)

Question 19

If an electric field is given as:

4y2z +10xyz + 8xy2  V/m.

And ΔL= -2 +4 - 3 μm.

Determine the work (in pJ) that is to be done in moving a 3μC charge along this path if the path is located at P(-0.3, -4, 0.6).

Question 20

The integral, , where C is the helical path described by , x = cos t, y = sin t, z = t, joining the points given by t = 0 and t = , comes as . calculate the value of P.

Question 21

Given electric field . Find the work done (in mJ) moving a –2 μC charge from (0, 5, 0) to (2, –1, 0) by taking the path (0, 5, 0) (2, 5, 0) (2, 1, 0) is______

Question 22

An insulating dielectric slab with 500 mm 500 mm cross section is 0.4 m long. A uniform electric field of 10 kV/mm is applied on the slab. The energy stored in the dielectric is…….J

(Relative permittivity of the material is 1.2)

Question 23

Given a vector field in Cartesian coordinates= The value of [where S is the surface of the cube defined by
0 is given by________

Question 24Multiple Correct Options

Which of the following can be a static electric field?

Question 25Multiple Correct Options

Which of the following Maxwell's equations of time varying fields is / are incorrect?
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