A wire loop P Q R having the shape of a right-angle triangle with P Q = 3 x , P R = 4 x and Q R = 5 x carries a steady current I . If the magnitude of the magnetic field at the point P   due to this loop is k μ 0 I 48 π x , t

Question

A wire loop P Q R having the shape of a right-angle triangle with P Q = 3 x , P R = 4 x and Q R = 5 x carries a steady current I . If the magnitude of the magnetic field at the point P &#160; due to this loop is k &#956; 0 I 48 &#960; x , then find the value of k .

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Correct answer: 7

The magnetic field at P due to current elements PQ and P R is zero as the point P is on the conductor. Therefore, the magnetic field at P due to current element Q R is B = μ 0 I 4 π ( P D ) s i n ϕ 1 + s i n ϕ 2 = μ 0 1 × 5 4 π × 12 x 9 x 5 3 x + 16 x 5 4 x = μ 0 I × 5 48 π x 3 5 + 4 5 = 7 48 μ 0 I π x

A wire loop P Q R having the shape of a right-angle triangle with P Q = 3 x , P R = 4 x and Q R = 5 x carries a steady current I . If the magnitude of the magnetic field at the point P   due to this loop is k μ 0 I 48 π x , then find the value of k .

Correct answer

Step-by-step solution

More from Magnetic Effects of Current

A wire loop P Q R having the shape of a right-angle triangle with P Q = 3 x , P R = 4 x and Q R = 5 x carries a steady current I . If the magnitude of the magnetic field at the point P &#160; due to this loop is k &#956; 0 I 48 &#960; x , then find the value of k .

Correct answer

Step-by-step solution

More from Magnetic Effects of Current

A wire loop P Q R having the shape of a right-angle triangle with P Q = 3 x , P R = 4 x and Q R = 5 x carries a steady current I . If the magnitude of the magnetic field at the point P due to this loop is k μ 0 I 48 π x , then find the value of k .