How to ask professors to serve on Ph.D. committee

I have to take the comprehensive exam in the near future and need to form a Ph.D. committee. With the help from Rahul, I came up with a succinct email for this.

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The format is

Hello Dr. [professor to ask],

I am a Ph.D. student working with Dr. [my advisor]. My work focuses on [very compact description of your thesis]. I was going through your research interests and found out about your expertise in [related expertise of professor to ask]. I would very much appreciate if you would agree to serve on my Ph.D. committee and guide me in my research. Would it be possible for you to serve on my PhD committee?

I look forward to your positive response.

Sincerely,
[my name]

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