Electromagnetic Theory [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 85 - 88 of 88

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Question 85

Appeared in Year: 2017

Describe in Detail

Essay▾

Light is incident from a medium of refractive index onto vacuum. The smallest angle of incident of which light is not transmitted into vacuum is . (up to two decimal places) .

Explanation

• The smallest angle of incident of which light is not transmitted into vacuum is critical angle .
• When we incident light at the angle of critical angle, the light is refracted along the intersection line of medium and vacuum. Therefore, refraction angle becomes .
• Applying Snell՚s law of refraction,

• Where, are the refractive index of medium and vacuum …

… (3 more words) …

Question 86

Appeared in Year: 2017

Describe in Detail

Essay▾

A parallel plate capacitor with square plates of side separated by is filled with a medium of dielectric constant of . If the charges on the two plates are and , the voltage across the capacitor is . (up to two decimal places) .

Explanation

According to question,

Area of the plate is,

Distance between two plates,

Dielectric constant is,

Charge on plates,

The capacitance of the capacitor is given as,

Now, capacitance of the capacitor is also given by,

Where, is the magnitude of charge on plate and is the voltage across the capacitor.

Question 87

Appeared in Year: 2017

Describe in Detail

Essay▾

Tree charges are placed at the vertices of an equilateral triangle of side as shown in the figure. The component of the electric dipole moment about the marked origin along the direction is .

Explanation

Here, the electric dipole moment is expressed by,

Where, is the displacement vector pointing from negative charge to the positive charge. The electric dipole moment vector is also having same direction as displacement vector .

From given situation, the charges of the dipole are and , separated by the distance (altitude of triangle ) . Therefore, r…

… (3 more words) …

Question 88

Electromagnetic Theory

Appeared in Year: 2017

Describe in Detail

Essay▾

A uniform volume charge density is placed inside a conductor (with resistivity ) . The charge density becomes of its original value after time seconds. (up to two decimal places)

Explanation

According to charge conservation law, the time rate of decrease of charge within a given volume equal to the net outward current flow through the closed surface of the volume.

Let, the current coming out of the closed surface is

Where, is the total charge enclosed by closed surface.

Applying divergence theorem,

But,

Therefore equation (1) become,

This …

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