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Shameem S.

Tutor for 3 years

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Physics (Electricity and Magnetism)

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Question:

A conducting straight wire of length 20 cm is moving with a constant speed of 5 m/s perpendicular to uniform 0.2 T magnetic field. The wire is perpendicular to the magnetic field. Calculate the voltage across the wire.

Shameem S.

Answer:

In this problem we need to use an expression for the induced voltage across the moving wire in uniform magnetic field. The voltage is given by the following expression E = B*L*v B=0.2T L=20cm=0.2m v= 5 m/s E=0.2*0.2*5 = 0.2 v

Trigonometry

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Question:

Prove the identity (1 + cos(x) + cos(2x)) / (sin(x) + sin(2x)) = cot(x)

Shameem S.

Answer:

Use the identities cos(2x) = 2 cos2(x) - 1 and sin(2x) = 2 sin(x) cos(x) in the left hand side of the given identity. [ 1 + cos(x) + cos(2x) ] / [ sin(x) + sin(2x) ] = [ 1 + cos(x) + 2 cos2(x) - 1 ] / [ sin(x) + 2 sin(x) cos(x) ] = [ cos(x) + 2 cos2(x) ] / [ sin(x) + 2 sin(x) cos(x) ] = cos(x) [1 + 2 cos(x)] / [ sin(x)( 1 + 2 cos(x) ) ] = cot(x)

Algebra

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Question:

Find the equation of the line that passes through the points (-1 , -1) and (-1 , 2).

Shameem S.

Answer:

To find the equation of the line through the points (-1 , -1) and (-1 , 2), we first use the slope m. m = (y2 - y1) / (x2 - x1) = (2 - -1) / (-1 - -1) = 3 / 0 The slope is indefined which means the line is perpendicular to the x axis and its equation has the form x = constant. Since both points have equal x coordinates -1, the equation is given by: x = -1

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