A uniform magnetic field of strength exists vertically downwards. These magnetic field lines pass through a closed surface as shown in the figure. The closed surface consists of a hemisphere , a right circular cone , and a circular surface . The magnetic flux through and are respectively
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Official Solution
Correct Option: (1)
Magnetic flux is defined as the product of the magnetic field strength and the area through which the field lines pass, considering the direction of the field relative to the area: For the magnetic flux through the hemisphere and the cone , the direction of the magnetic field and the area of each surface are important. - The magnetic flux through the hemisphere is negative because the area vector is opposite to the direction of the magnetic field. - The flux through the cone is positive because the area vector and the magnetic field are aligned.
Thus, the fluxes through the surfaces are:
02
PYQ 2026
medium
physicsID: kcet-202
What will be the total electric flux through the faces of the cube as given in the figure with side of length 'a' if a charge Q is placed at B, midpoint of an edge of the cube (see figure)?
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Official Solution
Correct Option: (3)
Step 1: Understanding the Question:
The question asks for the net electric flux through a single cube when a point charge is placed exactly at the midpoint of one of its edges. We can use Gauss's Law and symmetry to solve this. Step 2: Key Formula or Approach:
Gauss's Law states that the total flux through a closed surface is .
If a charge is on the boundary of a surface, we can construct a larger symmetrical surface consisting of identical units to enclose the charge completely. Step 3: Detailed Explanation:
1. The charge is placed at the midpoint of an edge.
2. To enclose this point charge completely and symmetrically, we need 4 such identical cubes sharing that same edge.
3. According to Gauss's Law, the total flux through this large composite surface (consisting of 4 cubes) is .
4. Since the charge is placed symmetrically with respect to all 4 cubes, the flux through each individual cube will be one-fourth of the total flux. Step 4: Final Answer:
The total electric flux through the faces of the cube is .
03
PYQ 2026
easy
physicsID: kcet-202
Consider three point charges and and three surfaces S , S and S as shown in the figure. Match the entries of List-I with that of List-II. List-I
(a) Net flux through S
(b) Net flux through S
(c) Net flux through S List-II
(i)
(ii)
(iii) Zero Codes:
1
a - ii, b - i, c - iii
2
a - iii, b - ii, c - i
3
a - i, b - ii, c - iii
4
a - ii, b - iii, c - i
Official Solution
Correct Option: (4)
Step 1: Understanding the Question:
The problem requires calculating the net electric flux through different Gaussian surfaces by identifying which charges are enclosed within each surface. Step 2: Key Formula or Approach:
By Gauss's Law, , where is the algebraic sum of charges inside the closed surface. Step 3: Detailed Explanation:
From the figure:
1. Surface S encloses the charges and .
Net flux through S = .
This matches with (ii).
2. Surface S encloses the charges and .
Net flux through S = .
This matches with (iii).
3. Surface S is the outermost surface and encloses all three charges: , and .
Net flux through S = .
This matches with (i).
Therefore, the correct matching is: a - ii, b - iii, c - i. Step 4: Final Answer:
The correct code is (4).
