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Electric and Magnetic Fields & Laws

11 Questions
GATE→2026→Electricity and Magnetism→Electric and Magnetic Fields & Laws
Q1
MCQ[1 Mark]
An electric field has a potential of V(x,y,z)=x2+y2+z2V(x,y,z) = \sqrt{x^{2}+y^{2}+z^{2}} V. A charge of 1 coulomb placed at (i^+j^+k^)(\hat{i}+\hat{j}+\hat{k}) experiences a force of F⃗=(ai^+bj^+ck^)\vec{F} = (a\hat{i}+b\hat{j}+c\hat{k}) N. The values of (a, b, c) are
GATE→2026→Electricity and Magnetism→Electric and Magnetic Fields & Laws
Q2
NAT[1 Mark]
The potential difference between nodes A and B in a circuit is vA−vB=5v_{A} - v_{B} = 5 V. The work done in moving a charge of 1 coulomb from point B to A is J. (answer in integer)
GATE→2026→Electricity and Magnetism→Electric and Magnetic Fields & Laws
Q3
MCQ[2 Marks]
An electric field in free space is E⃗=(2x+5y+6z)i^+(5x+4y+10z)j^+(6x+10y+2z)k^\vec{E} = (2x+5y+6z)\hat{i} + (5x+4y+10z)\hat{j} + (6x+10y+2z)\hat{k} V/m. The charge density is ϵ0\epsilon_{0} is the permittivity of free space)
GATE→2026→Electricity and Magnetism→Electric and Magnetic Fields & Laws
Q4
MCQ[2 Marks]
A straight thin wire carrying a current of I=1I = 1 A in the direction n^=16i^+26j^+16k^\hat{n} = \frac{1}{\sqrt{6}}\hat{i} + \frac{2}{\sqrt{6}}\hat{j} + \frac{1}{\sqrt{6}}\hat{k} is placed inside a magnetic field of B⃗=(2i^+2k^)\vec{B} = (2\hat{i} + 2\hat{k}) T. The force per unit length on the wire is N/m.
GATE→2025→Electricity and Magnetism→Electric and Magnetic Fields & Laws
Q5
MCQ[1 Mark]
An infinite sheet of uniform charge ρs=10 C/m2\rho_{s} = 10 \text{ C/m}^{2} is placed on z=0z = 0 plane. The medium surrounding the sheet has a relative permittivity of 10. The electric flux density, in C/m2\text{C/m}^{2}, at a point P(0,0,5)P(0,0,5), is
GATE→2025→Electricity and Magnetism→Electric and Magnetic Fields & Laws
Q6
MCQ[1 Mark]
A 60 V DC source with an internal resistance Rint=0.5R_{int} = 0.5 \Omega is connected through a switch to a pair of infinitely long rails separated by l=1l = 1 m as shown in the figure. The rails are placed in a constant, uniform magnetic field of flux density B=0.5B = 0.5 T, directed into the page. A conducting bar placed on these rails is free to move. At the instant of closing the switch, the force induced on the bar is
GATE→2024→Electricity and Magnetism→Electric and Magnetic Fields & Laws
Q7
MCQ[1 Mark]
The capacitance formed between two concentric spherical metal shells having radii x and y with y>xy > x is
GATE→2024→Electricity and Magnetism→Electric and Magnetic Fields & Laws
Q8
MCQ[2 Marks]
A wire of circular cross section with radius a is shown in the figure. The current density is given by J=ks2J = ks^{2}, where k is a constant, s is the radial distance from the axis and 0≤s≤a0 \le s \le a. The total current I in the wire is
Figure for Question 8
GATE→2023→Electricity and Magnetism→Electric and Magnetic Fields & Laws
Q9
NAT[1 Mark]
The force per unit length between two infinitely long parallel conductors, with a gap of 2 cm between them is 10 \mu\text{N/m}. When the gap is doubled, the force per unit length will be \mu\text{N/m} (rounded off to one decimal place).
GATE→2022→Electricity and Magnetism→Electric and Magnetic Fields & Laws
Q10
NAT[2 Marks]
A conducting semi-circular loop of radius R=0.1R = 0.1 m... the peak-to-peak current (in milliamperes) in the loop is (round off to one decimal place).
Figure for Question 10
GATE→2022→Electricity and Magnetism→Electric and Magnetic Fields & Laws
Q11
NAT[2 Marks]
A capacitor is constructed using two concentric spheres and air as the dielectric medium... The capacitance (in picofarads) is (round off to 2 decimal places).