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GATE EE 2023
MCQ (More than One Correct Answer)
+2
-0

In the figure, the electric field E and the magnetic field B point to x and z directions, respectively, and have constant magnitudes. A positive charge 'q' is released from rest at the origin. Which of the following statement(s) is/are true.

GATE EE 2023 Electromagnetic Fields - Magnetostatics Question 3 English

A
The charge will move in the direction of z with constant velocity.
B
The charge will always move on the y-z plane only.
C
The trajectory of the charge will be a circle.
D
The charge will progress in the direction of y.
2
GATE EE 2023
Numerical
+2
-0

An infinite surface of linear current density $$K = 5{\widehat a_x}$$ A/m exists on the x-y plane, as shown in the figure. The magnitude of the magnetic field intensity (H) at a point (1, 1, 1) due to the surface current in Ampere/meter is ____________ (Round off to 2 decimal places).

GATE EE 2023 Electromagnetic Fields - Magnetostatics Question 2 English

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3
GATE EE 2023
Numerical
+2
-0

The closed curve shown in the figure is described by

$$r = 1 + \cos \theta $$, where $$r = \sqrt {{x^2} + {y^2}} ;x = r\cos \theta ,y = r\sin \theta $$

The magnitude of the line integral of the vector field $$F = - y\widehat i + x\widehat j$$ around the closed curve is ___________ (Round off to 2 decimal places).

GATE EE 2023 Electromagnetic Fields - Electrostatics Question 4 English

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4
GATE EE 2023
Numerical
+2
-0

A quadratic function of two variables is given as

$$f({x_1},{x_2}) = x_1^2 + 2x_2^2 + 3{x_1} + 3{x_2} + {x_1}{x_2} + 1$$

The magnitude of the maximum rate of change of the function at the point (1, 1) is ___________ (Round off to the nearest integer).

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